{"id":9747,"date":"2026-07-25T20:26:26","date_gmt":"2026-07-25T11:26:26","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9747"},"modified":"2026-07-27T15:54:22","modified_gmt":"2026-07-27T06:54:22","slug":"math-abstraction-07-topological-spaces","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/mathematical-abstraction\/math-abstraction-07-topological-spaces\/","title":{"rendered":"\uac70\ub9ac\uacf5\uac04\uacfc \uc704\uc0c1\uacf5\uac04"},"content":{"rendered":"<p><!-- \uc218\ud559\uc801 \ucd94\uc0c1\ud654 7\ud3b8: \uac70\ub9ac\uc5d0\uc11c \uc704\uc0c1\uc73c\ub85c --><\/p>\n<div class=\"math-abs-series\">\n<p><a href=\"..\/math-abstraction-06-vector-spaces\/\">6\ubd80<\/a>\uc758 \ub9d0\ubbf8\uc5d0\uc11c \uc644\ube44\uc131\uc744 \uc815\uc758\ud560 \ub54c, \uc6b0\ub9ac\ub294 \u2018\ucf54\uc2dc\uc218\uc5f4\uc774 \uc5b4\ub5a4 \uc810\uc73c\ub85c \uc218\ub834\ud55c\ub2e4\u2019\ub294 \uc870\uac74\uc744 \uc0ac\uc6a9\ud588\ub2e4. \uadf8\ub7f0\ub370 \u2018\uc218\ub834\ud55c\ub2e4\u2019, \uace7 \ud55c \uc810\uc5d0 \u2018\uac00\uae4c\uc6cc\uc9c4\ub2e4\u2019\ub294 \ub9d0\uc774 \uc815\ud655\ud788 \ubb34\uc5c7\uc744 \ub73b\ud558\ub294\uc9c0\ub294 \uae4a\uc774 \ub2e4\ub8e8\uc9c0 \uc54a\uc558\ub2e4. \uc2e4\ud574\uc11d\uc5d0\uc11c \uac00\uae4c\uc6c0\uc744 \ub098\ud0c0\ub0b4\ub294 \uac00\uc7a5 \uc775\uc219\ud55c \ubaa8\ud615\uc740 \uc2e4\uc9c1\uc120 \uc704\uc758 \uac70\ub9ac \\(|x-y|\\)\uc774\ub2e4. \uadf8\ub7ec\ub098 \ud568\uc218\ub098 \uc218\uc5f4\ucc98\ub7fc \ub354 \uc77c\ubc18\uc801\uc778 \ub300\uc0c1\uc744 \ub2e4\ub8e8\ub824\uba74 \ubb34\uc5c7\uc744 \uac70\ub9ac\ub85c \uc0bc\uc744\uc9c0\ubd80\ud130 \uc0c8\ub85c \uc815\ud574\uc57c \ud558\uba70, \uc5b4\ub5a4 \uacf5\uac04\uc758 \uc790\uc5f0\uc2a4\ub7ec\uc6b4 \uac00\uae4c\uc6c0\uc740 \uc544\uc608 \ud558\ub098\uc758 \uac70\ub9ac\ub85c \ud45c\ud604\ub418\uc9c0 \uc54a\uae30\ub3c4 \ud55c\ub2e4. \uc774 \uae00\uc5d0\uc11c\ub294 \uc2e4\uc218\uc758 \uac70\ub9ac\uc5d0\uc11c \uac70\ub9ac\uacf5\uac04\uc73c\ub85c, \ub2e4\uc2dc \uc704\uc0c1\uacf5\uac04\uc73c\ub85c \ub098\uc544\uac00\ub294 \uacfc\uc815\uc744 \uc0b4\ud3b4\ubcf8\ub2e4. \ub610\ud55c \ud2b9\uc815 \uacf5\uac04\uc5d0\uc11c \uc99d\uba85\ub41c \uc131\uc9c8\uc774 \ub354 \uc77c\ubc18\uc801\uc778 \uacf5\uac04\uc744 \ubd84\ub958\ud558\ub294 \uc815\uc758\ub85c \ucc44\ud0dd\ub418\ub294 \uacfc\uc815\uc744 \ucef4\ud329\ud2b8\uc131\uacfc \uc5f0\uacb0\uc131\uc758 \uc0ac\ub840\ub97c \ud1b5\ud574 \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n<h4>\ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4\uc640 \u03b5-\u03b4 \ub17c\ubc95<\/h4>\n<p>\ubd80\ubd84\uc9d1\ud569 \\(D\\subseteq\\mathbb R\\)\uc5d0\uc11c \uc815\uc758\ub41c \ud568\uc218 \\(f:D\\to\\mathbb R\\)\uac00 \uc810 \\(x_0\\in D\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ub77c\ub294 \uc0ac\uc2e4\uc744 \uc624\ub298\ub0a0\uc5d0\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ud45c\ud604\ud55c\ub2e4. \uc784\uc758\uc758 \\(\\varepsilon>0\\)\uc5d0 \ub300\ud558\uc5ec \uc5b4\ub5a4 \\(\\delta>0\\)\uac00 \uc874\uc7ac\ud558\uc5ec, \ubaa8\ub4e0 \\(x\\in D\\)\uc5d0 \ub300\ud574<br \/>\n\\[<br \/>\n|x-x_0|<\\delta\\ \\Longrightarrow\\ |f(x)-f(x_0)|<\\varepsilon\n\\]\n\uac00 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<p>\uc774\ub7ec\ud55c \uc5c4\ubc00\ud55c \uc218\ud559\uc801 \ud45c\ud604\uc740 \uc5ec\ub7ec \uc218\ud559\uc790\uc758 \uc190\uc744 \uac70\uce58\uba70 \uc11c\uc11c\ud788 \ub2e4\ub4ec\uc5b4\uc84c\ub2e4. \ubcfc\ucc28\ub178(Bernard Bolzano)\ub294 1817\ub144 \uc5f0\uc18d\uc131\uacfc \uc911\uac04\uac12 \uc131\uc9c8\uc744 \ubd80\ub4f1\uc2dd\uc73c\ub85c \uc5c4\ubc00\ud558\uac8c \ub2e4\ub8e8\ub824 \ud588\uace0, \ucf54\uc2dc(Augustin-Louis Cauchy)\ub294 1821\ub144 \u300e\ud574\uc11d\ud559 \uac15\uc758\u300f(<i>Cours d\u2019Analyse<\/i>)\uc5d0\uc11c \ubcc0\uc218\uc758 \ubb34\ud55c\uc18c \uc99d\ubd84\uc5d0 \ub300\uc751\ud558\ub294 \ud568\uc218\uac12\uc758 \ubb34\ud55c\uc18c \ubcc0\ud654\ub97c \ud1b5\ud574 \uc5f0\uc18d\uc131\uc744 \uc124\uba85\ud588\ub2e4.<!-- \ucf54\uc2dc\uc758 \uc800\uc220\uc5d0\ub294 \uc774\ubbf8 \ubd80\ub4f1\uc2dd\uc744 \uc774\uc6a9\ud55c \uc815\uad50\ud55c \ub17c\uc99d\uc774 \uc788\uc5c8\uc9c0\ub9cc, \ud604\ub300 \uad50\uacfc\uc11c\uc640 \uac19\uc740 \uc591\ud654\uc0ac \uad6c\uc870\uc758 \u03b5-\u03b4 \uc815\uc758\uac00 \uadf8\ub300\ub85c \uc81c\uc2dc\ub41c \uac83\uc740 \uc544\ub2c8\uc5c8\ub2e4. 19\uc138\uae30 \uc804\ubc18\uc5d0 \ucd95\uc801\ub41c \uc774\ub7ec\ud55c \uc791\uc5c5\uc740 \ub9ac\ub9cc\uacfc \ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4\uc758 \uc5f0\uad6c \ubc0f \uac15\uc758\ub97c \uac70\uce58\uba70 \uc624\ub298\ub0a0\uc758 \uc0b0\uc220\uc801 \uc5c4\ubc00\uc131\uc73c\ub85c \uc810\ucc28 \uc815\ub9ac\ub418\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Grabiner, J. V. (1983). \u201cWho Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus.\u201d The American Mathematical Monthly, 90(3), 185\u2013194. Claremont Colleges Scholarship.\" href=\"#ref-Grabiner1983\">[Grabiner1983]<\/a> --><\/p>\n<p>\uce74\ub97c \ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4(Karl Weierstrass)\ub294 1860\ub144\ub300 \ubca0\ub97c\ub9b0 \ub300\ud559 \uac15\uc758\uc5d0\uc11c \uadf9\ud55c\uacfc \uc5f0\uc18d\uc131\uc744 \u03b5\uc640 \u03b4\ub97c \uc0ac\uc6a9\ud55c \ubd80\ub4f1\uc2dd\uc758 \uc5b8\uc5b4\ub85c \uccb4\uacc4\uc801\uc73c\ub85c \uc804\uac1c\ud588\ub2e4. \uc5ec\uae30\uc11c \ud575\uc2ec\uc740 \ubaa8\ud638\ud55c \ud06c\uae30\uc758 \u2018\ubb34\ud55c\uc18c\u2019\ub97c \uc9c1\uc811 \uc870\uc791\ud558\ub294 \ub300\uc2e0, \uc784\uc758\ub85c \uc8fc\uc5b4\uc9c4 \uc591\uc758 \uc624\ucc28 \\(\\varepsilon\\)\uc5d0 \ub300\uc751\ud558\ub294 \uc591\uc758 \ud5c8\uc6a9 \ubc94\uc704 \\(\\delta\\)\ub97c \ucc3e\ub294 \ub370 \uc788\ub2e4. <!-- \ub2e4\ub9cc \ud574\uc11d\ud559\uc758 \uc5c4\ubc00\ud654\ub97c \ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4 \ud55c \uc0ac\ub78c\uc758 \ub2e8\ub3c5 \uc5c5\uc801\uc73c\ub85c \ub3cc\ub9ac\uae30\ubcf4\ub2e4\ub294, \ucf54\uc2dc\ub97c \ube44\ub86f\ud55c 19\uc138\uae30 \uc218\ud559\uc790\ub4e4\uc758 \ubd80\ub4f1\uc2dd \uae30\ubc95\uc774 \ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4 \ud559\ud30c\uc5d0\uc11c \uccb4\uacc4\ud654\ub418\uc5c8\ub2e4\uace0 \ubcf4\ub294 \ud3b8\uc774 \uc5ed\uc0ac\uc801\uc73c\ub85c \uc815\ud655\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Grabiner, J. V. (1983). \u201cWho Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus.\u201d The American Mathematical Monthly, 90(3), 185\u2013194. Claremont Colleges Scholarship.\" href=\"#ref-Grabiner1983\">[Grabiner1983]<\/a> --><\/p>\n<p>[\ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4\ub294 \uc774 \uccb4\uacc4\ub97c \ub2f4\uc740 \ud574\uc11d\ud559 \uad50\uacfc\uc11c\ub97c \uc9c1\uc811 \ucd9c\ud310\ud558\uc9c0 \uc54a\uc558\ub2e4. \uadf8\uc758 \uc774\ub860\uc740 \ud559\uc0dd\ub4e4\uc758 \uac15\uc758 \ud544\uae30\uc640 \ud6c4\uc18d \ubb38\ud5cc\uc744 \ud1b5\ud574 \ub110\ub9ac \uc804\ud574\uc84c\ub2e4. \ud558\uc774\ub124(Eduard Heine)\uc758 1872\ub144 \ub17c\ubb38\ub3c4 \uac19\uc740 \uc5c4\ubc00\ud654 \ud750\ub984\uc758 \uc911\uc694\ud55c \ucd9c\ud310\ubb3c\uc774\uc9c0\ub9cc, \ud558\uc774\ub124\ub294 \ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4\uc758 \uc81c\uc790\uac00 \uc544\ub2c8\uc5c8\ub2e4. <!-- \ub530\ub77c\uc11c \uc624\ub298\ub0a0\uc758 \uc815\uc758\ub97c \ud2b9\uc815 \uac15\uc758\uc758 \ud55c \ubb38\uc7a5\uacfc \ub3d9\uc77c\uc2dc\ud558\uae30\ubcf4\ub2e4\ub294, 19\uc138\uae30 \ud6c4\ubc18\uc758 \uac15\uc758\uc640 \ucd9c\ud310\uc744 \ud1b5\ud574 \uccb4\uacc4\ud654\u00b7\ud655\uc0b0\ub41c \uc815\uc2dd\ud654\ub85c \uc774\ud574\ud558\ub294 \uac83\uc774 \uc548\uc804\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Grabiner, J. V. (1983). \u201cWho Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus.\u201d The American Mathematical Monthly, 90(3), 185\u2013194. Claremont Colleges Scholarship.\" href=\"#ref-Grabiner1983\">[Grabiner1983]<\/a>] --><\/p>\n<p>\uc774 \uc815\uc758\uc5d0\ub294 \\(|x-x_0|\\)\uc640 \\(|f(x)-f(x_0)|\\)\ub77c\ub294 \ub450 \uac70\ub9ac\uac00 \ub4e4\uc5b4 \uc788\ub2e4. \uc808\ub313\uac12\uc740 \uc2e4\uc9c1\uc120\uc5d0\uc11c \ub450 \uc810 \uc0ac\uc774\uc758 \uac70\ub9ac\ub97c \ub098\ud0c0\ub0b4\uc9c0\ub9cc, \ud568\uc218\u00b7\uc218\uc5f4\u00b7\uae30\ud558\ud559\uc801 \ud615\uc0c1\ucc98\ub7fc \uc6d0\uc18c\uc758 \uc885\ub958\uac00 \ub2ec\ub77c\uc9c0\uba74 \uac00\uae4c\uc6c0\uc744 \uc7ac\ub294 \uaddc\uce59\ub3c4 \ub2ec\ub77c\uc838\uc57c \ud55c\ub2e4. <!-- \uc774\ub54c \ud544\uc694\ud55c \uac83\uc740 \uc2e4\uc218\uc758 \ud2b9\ubcc4\ud55c \uc131\uc9c8\uc744 \ubaa8\ub450 \ubcf4\uc874\ud558\ub294 \uc77c\uc774 \uc544\ub2c8\ub77c, \u2018\uac70\ub9ac\ub2f5\uac8c \ud589\ub3d9\ud558\ub294 \ub370 \ud544\uc694\ud55c \uc870\uac74\u2019\ub9cc \uac00\ub824\ub0b4\ub294 \uc77c\uc774\ub2e4. --><\/p>\n<h4>\ud504\ub808\uc170, \uac70\ub9ac\uc758 \uacf5\ub9ac\ub9cc \ub0a8\uae30\ub2e4<\/h4>\n<p>\ubaa8\ub9ac\uc2a4 \ud504\ub808\uc170(Maurice Fr\u00e9chet)\ub294 1906\ub144 \ubc15\uc0ac\ud559\uc704 \ub17c\ubb38 \u300c\ud568\uc218 \uacc4\uc0b0\uc758 \uba87 \uac00\uc9c0 \ubb38\uc81c\uc5d0 \ub300\ud558\uc5ec\u300d(<i>Sur quelques points du calcul fonctionnel<\/i>)\uc5d0\uc11c \ud568\uc218\uc640 \uac19\uc740 \uc77c\ubc18\uc801 \ub300\uc0c1\uc744 \ub2e4\ub8f0 \uc218 \uc788\ub3c4\ub85d \ucd94\uc0c1 \uacf5\uac04, \uc218\ub834, \ucef4\ud329\ud2b8\uc131\uc758 \uac1c\ub150\uc744 \uc5f0\uad6c\ud588\ub2e4. \ud2b9\ud788 \uadf8\uc758 \u2018\uac70\ub9ac(\u00e9cart)\u2019 \uac1c\ub150\uc740 \uc810\uc758 \uc815\uccb4\uc640 \ubb34\uad00\ud558\uac8c \ub450 \uc810 \uc0ac\uc774\uc758 \uac00\uae4c\uc6c0\uc744 \uacf5\ub9ac\ub85c \ub2e4\ub8e8\ub294 \uae38\uc744 \uc5f4\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Fr\u00e9chet, M. (1906). \u201cSur quelques points du calcul fonctionnel.\u201d Rendiconti del Circolo Matematico di Palermo, 22, 1\u201372.\" href=\"#ref-Frechet1906\">[Frechet1906]<\/a><a class=\"math-abs-series-ref\" title=\"Taylor, A. E. (1982). \u201cA Study of Maurice Fr\u00e9chet: I. His Early Work on Point Set Theory and the Theory of Functionals.\u201d Archive for History of Exact Sciences, 27, 233\u2013295.\" href=\"#ref-Taylor1982\">[Taylor1982]<\/a><\/p>\n<p>[\ud504\ub808\uc170\ub294 \uc218\uc5f4\uc758 \uc218\ub834\uc744 \uc9c1\uc811 \uacf5\ub9ac\ud654\ud55c \\(L\\)\ub958, \uadfc\uc811\ud568\uc218\ub97c \uc0ac\uc6a9\ud55c \\(V\\)\ub958, \u2018\uac04\uaca9(\u00e9cart)\u2019\uc5d0 \uc0bc\uac01\ubd80\ub4f1\uc2dd\uc744 \uc694\uad6c\ud55c \\(E\\)\ub958 \ub4f1 \uc5ec\ub7ec \uc885\ub958\uc758 \ucd94\uc0c1 \uacf5\uac04\uc744 \ud568\uaed8 \uc5f0\uad6c\ud588\ub2e4. \uc774 \uac00\uc6b4\ub370 \\(E\\)\ub958\uc758 \uc870\uac74\uc740 \ud604\ub300 \uac70\ub9ac\uacf5\uac04\uc758 \uacf5\ub9ac\uc640 \ubcf8\uc9c8\uc801\uc73c\ub85c \uac19\ub2e4. \u2018\uac70\ub9ac\uacf5\uac04(metric space)\u2019\uc774\ub77c\ub294 \uba85\uce6d\uacfc \uc775\uc219\ud55c \uad50\uacfc\uc11c\uc801 \uc815\uc2dd\ud654\ub294 \ud558\uc6b0\uc2a4\ub3c4\ub974\ud504\uc758 1914\ub144 \uc800\uc11c\ub97c \uac70\uce58\uba70 \uc815\ucc29\ub418\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Fr\u00e9chet, M. (1906). \u201cSur quelques points du calcul fonctionnel.\u201d Rendiconti del Circolo Matematico di Palermo, 22, 1\u201372.\" href=\"#ref-Frechet1906\">[Frechet1906]<\/a><a class=\"math-abs-series-ref\" title=\"Taylor, A. E. (1982). \u201cA Study of Maurice Fr\u00e9chet: I. His Early Work on Point Set Theory and the Theory of Functionals.\u201d Archive for History of Exact Sciences, 27, 233\u2013295.\" href=\"#ref-Taylor1982\">[Taylor1982]<\/a><a class=\"math-abs-series-ref\" title=\"Hausdorff, F. (1914). Grundz\u00fcge der Mengenlehre. Leipzig: Veit &amp; Comp. \uc6d0\ubb38 \uc2a4\uce94: Internet Archive.\" href=\"#ref-Hausdorff1914\">[Hausdorff1914]<\/a>]<\/p>\n<p>\ud604\ub300\uc801\uc778 \uc815\uc758\ub97c \uc4f0\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4. \uc9d1\ud569 \\(X\\) \uc704\uc758 \ud568\uc218 \\(d:X\\times X\\to[0,\\infty)\\)\uac00 \ubaa8\ub4e0 \\(x,y,z\\in X\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud560 \ub54c \\(d\\)\ub97c \\(X\\) \uc704\uc758 <span class=\"defined\">\uac70\ub9ac<\/span>(metric)\ub77c\uace0 \ud55c\ub2e4.<\/p>\n<ul>\n<li>\\(d(x,y)=0\\Longleftrightarrow x=y\\)<\/li>\n<li>\\(d(x,y)=d(y,x)\\)<\/li>\n<li>\\(d(x,z)\\le d(x,y)+d(y,z)\\)<\/li>\n<\/ul>\n<p>\uc138 \ubc88\uc9f8 \uc870\uac74\uc740 <span class=\"defined\">\uc0bc\uac01\ubd80\ub4f1\uc2dd<\/span>(triangle inequality)\uc774\ub2e4. \uac70\ub9ac\uc640 \uc9d1\ud569\uc758 \uc21c\uc11c\uc30d \\((X,d)\\)\ub97c <span class=\"defined\">\uac70\ub9ac\uacf5\uac04<\/span>(metric space)\uc774\ub77c\uace0 \ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4 \ub2eb\ud78c\uad6c\uac04 \\([a,b]\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc2e4\uc218\uac12 \uc5f0\uc18d\ud568\uc218\ub4e4\uc758 \uc9d1\ud569 \\(C([a,b])\\)\uc5d0\ub294<br \/>\n\\[<br \/>\nd_\\infty(f,g)=\\sup_{x\\in[a,b]}|f(x)-g(x)|<br \/>\n\\]<br \/>\n\ub77c\ub294 \uac70\ub9ac\ub97c \uc904 \uc218 \uc788\ub2e4. \uc5f0\uc18d\ud568\uc218\ub294 \ucef4\ud329\ud2b8 \uad6c\uac04\uc5d0\uc11c \uc720\uacc4\uc774\ubbc0\ub85c \uc774 \uc0c1\ud55c\uc740 \uc720\ud55c\ud558\ub2e4. \ub610\ud55c \uc2e4\uc218\uc5f4 \uc804\uccb4\uc758 \uc9d1\ud569 \\(\\mathbb R^{\\mathbb N}\\)\uc5d0\ub294<br \/>\n\\[<br \/>\nd(x,y)=\\sum_{n=1}^{\\infty}2^{-n}\\min\\{1,|x_n-y_n|\\}<br \/>\n\\]<br \/>\n\ub77c\ub294 \uac70\ub9ac\ub97c \uc904 \uc218 \uc788\ub2e4. \uc774 \uac70\ub9ac\uc5d0\uc11c\uc758 \uc218\ub834\uc740 \uac01 \uc88c\ud45c\uc5d0\uc11c\uc758 \uc218\ub834\uacfc \uc815\ud655\ud788 \uc77c\uce58\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<p>[\uc0c1\ud55c \uac70\ub9ac\uc758 \uc0bc\uac01\ubd80\ub4f1\uc2dd\uc740 \uac01 \\(x\\in[a,b]\\)\uc5d0\uc11c<br \/>\n\\[<br \/>\n|f(x)-h(x)|\\le |f(x)-g(x)|+|g(x)-h(x)|<br \/>\n\\]<br \/>\n\uac00 \uc131\ub9bd\ud55c\ub2e4\ub294 \uc0ac\uc2e4\uc5d0\uc11c \ub098\uc628\ub2e4. \uc591\ubcc0\uc758 \uc0c1\ud55c\uc744 \ucde8\ud558\uba74<br \/>\n\\[<br \/>\nd_\\infty(f,h)\\le d_\\infty(f,g)+d_\\infty(g,h)<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4.]<\/p>\n<p>\uc774\uc81c \uc6d0\uc18c\uac00 \uc2e4\uc218\uc778\uc9c0 \ud568\uc218\uc778\uc9c0 \uc218\uc5f4\uc778\uc9c0\ub294 \uc911\uc694\ud558\uc9c0 \uc54a\ub2e4. \ub450 \uac70\ub9ac\uacf5\uac04 \\((X,d_X)\\), \\((Y,d_Y)\\) \uc0ac\uc774\uc758 \ud568\uc218 \\(F:X\\to Y\\)\uac00 \\(x_0\\in X\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ub77c\ub294 \uac83\uc740, \uc784\uc758\uc758 \\(\\varepsilon>0\\)\uc5d0 \ub300\ud558\uc5ec \uc5b4\ub5a4 \\(\\delta>0\\)\uac00 \uc874\uc7ac\ud558\uc5ec<br \/>\n\\[<br \/>\nd_X(x,x_0)<\\delta\\ \\Longrightarrow\\ d_Y(F(x),F(x_0))<\\varepsilon\n\\]\n\uac00 \uc131\ub9bd\ud55c\ub2e4\ub294 \ub73b\uc774\ub2e4. \ud568\uc218\uacf5\uac04\uc774\ub098 \ubca1\ud130\uacf5\uac04 \uc0ac\uc774\uc758 \uc0ac\uc0c1\uc778 \uc5f0\uc0b0\uc790(operator)\uc758 \uc5f0\uc18d\uc131\ub3c4 \uc774 \ud2c0\uc5d0\uc11c \uc815\uc758\ud560 \uc218 \uc788\ub2e4.<\/p>\n<h4>\ud558\uc6b0\uc2a4\ub3c4\ub974\ud504\uc640 \uac70\ub9ac \ub108\uba38\uc758 \uacf5\uac04<\/h4>\n<p>\ud3a0\ub9ad\uc2a4 \ud558\uc6b0\uc2a4\ub3c4\ub974\ud504(Felix Hausdorff)\ub294 1914\ub144 \u300e\uc9d1\ud569\ub860\uc758 \uae30\ucd08\u300f(<i>Grundz\u00fcge der Mengenlehre<\/i>)\uc5d0\uc11c \uc810\ub4e4\uc758 \uadfc\ubc29\uc744 \uacf5\ub9ac\ud654\ud558\uc5ec \uc77c\ubc18 \uacf5\uac04\uc744 \uccb4\uacc4\uc801\uc73c\ub85c \uc5f0\uad6c\ud588\ub2e4. \uc774\uac83\uc740 \ub450 \uc810 \uc0ac\uc774\uc758 \uac70\ub9ac\ub97c \uc218\uce58\ub85c \uc7ac\uc9c0 \uc54a\uace0\ub3c4 \uc218\ub834\uacfc \uc5f0\uc18d\uc131\uc744 \ub2e4\ub8f0 \uc218 \uc788\uc74c\uc744 \ubcf4\uc5ec \uc900 \uc911\uc694\ud55c \ub2e8\uacc4\uc600\ub2e4.<a class=\"math-abs-series-ref\" title=\"Hausdorff, F. (1914). Grundz\u00fcge der Mengenlehre. Leipzig: Veit &amp; Comp. \uc6d0\ubb38 \uc2a4\uce94: Internet Archive.\" href=\"#ref-Hausdorff1914\">[Hausdorff1914]<\/a><\/p>\n<p>[\ud558\uc6b0\uc2a4\ub3c4\ub974\ud504\uc758 \uc6d0\ub798 \uadfc\ubc29 \uacf5\ub9ac\uc5d0\ub294 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc810\uc744 \uc11c\ub85c\uc18c \uadfc\ubc29\uc73c\ub85c \ubd84\ub9ac\ud558\ub294 \uc870\uac74, \uace7 \uc624\ub298\ub0a0\uc758 \\(T_2\\) \uc870\uac74\uc774 \ud3ec\ud568\ub418\uc5b4 \uc788\uc5c8\ub2e4. \ud604\ub300\uc758 \uc5f4\ub9b0\uc9d1\ud569 \uacf5\ub9ac\ub294 \uadf8 \uc800\uc11c\uc5d0 \uc9c0\uae08\uacfc \ub611\uac19\uc740 \ud615\uc2dd\uc73c\ub85c \uc644\uc131\ub418\uc5b4 \uc788\uc5c8\ub358 \uac83\uc774 \uc544\ub2c8\ub77c, \uadfc\ubc29\u00b7\uc5f4\ub9b0\uc9d1\ud569\u00b7\ud3d0\ud3ec\ub97c \uc774\uc6a9\ud55c \uc5ec\ub7ec \ub3d9\uce58\uc801 \ud615\uc2dd\uc774 \uc815\ub9ac\ub418\ub294 \uacfc\uc815\uc5d0\uc11c \ud45c\uc900\ud654\ub418\uc5c8\ub2e4. \ucfe0\ub77c\ud1a0\ud504\uc2a4\ud0a4(Kazimierz Kuratowski)\uc758 1922\ub144 \ud3d0\ud3ec \uacf5\ub9ac\ub294 \uc774 \uacfc\uc815\uc758 \uc911\uc694\ud55c \uc774\uc815\ud45c \uac00\uc6b4\ub370 \ud558\ub098\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Hausdorff, F. (1914). Grundz\u00fcge der Mengenlehre. Leipzig: Veit &amp; Comp. \uc6d0\ubb38 \uc2a4\uce94: Internet Archive.\" href=\"#ref-Hausdorff1914\">[Hausdorff1914]<\/a><a class=\"math-abs-series-ref\" title=\"Kuratowski, C. (1922). \u201cSur l\u2019op\u00e9ration \u0100 de l\u2019Analysis Situs.\u201d Fundamenta Mathematicae, 3, 182\u2013199. \uc6d0\ubb38: EuDML.\" href=\"#ref-Kuratowski1922\">[Kuratowski1922]<\/a>]<\/p>\n<p>\ud604\ub300\uc801\uc778 \uc815\uc758\ub85c, \uc9d1\ud569 \\(X\\)\uc758 \ubd80\ubd84\uc9d1\ud569\ub4e4\uc758 \uc871 \\(\\tau\\)\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud55c\ub2e4\uace0 \ud558\uc790.<\/p>\n<ul>\n<li>\\(\\varnothing,X\\in\\tau\\).<\/li>\n<li>\\(\\tau\\)\uc5d0 \uc18d\ud558\ub294 \uc784\uc758\uc758 \ubd80\ubd84\uc871\uc758 \ud569\uc9d1\ud569\uc740 \\(\\tau\\)\uc5d0 \uc18d\ud55c\ub2e4.<\/li>\n<li>\\(\\tau\\)\uc5d0 \uc18d\ud558\ub294 \uc720\ud55c \uac1c \uc9d1\ud569\uc758 \uad50\uc9d1\ud569\uc740 \\(\\tau\\)\uc5d0 \uc18d\ud55c\ub2e4.<\/li>\n<\/ul>\n<p>\uc774\ub54c \\(\\tau\\)\ub97c \\(X\\) \uc704\uc758 <span class=\"defined\">\uc704\uc0c1<\/span>(topology), \\(\\tau\\)\uc758 \uc6d0\uc18c\ub97c <span class=\"defined\">\uc5f4\ub9b0\uc9d1\ud569<\/span>(open set), \uc21c\uc11c\uc30d \\((X,\\tau)\\)\ub97c <span class=\"defined\">\uc704\uc0c1\uacf5\uac04<\/span>(topological space)\uc774\ub77c\uace0 \ud55c\ub2e4. \uc815\uc758\uc5d0\ub294 \uac70\ub9ac\ub098 \uc218\uce58\uac00 \ub098\ud0c0\ub098\uc9c0 \uc54a\uace0, \uc5b4\ub5a4 \ubd80\ubd84\uc9d1\ud569\uc744 \uc5f4\ub9b0 \uac83\uc73c\ub85c \ubcfc\uc9c0\ub9cc \ub0a8\ub294\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<p>\ub450 \uc704\uc0c1\uacf5\uac04 \\((X,\\tau_X)\\), \\((Y,\\tau_Y)\\) \uc0ac\uc774\uc758 \ud568\uc218 \\(F:X\\to Y\\)\uc5d0 \ub300\ud558\uc5ec, \ubaa8\ub4e0 \uc5f4\ub9b0\uc9d1\ud569 \\(V\\in\\tau_Y\\)\uc758 \uc6d0\uc0c1 \\(F^{-1}(V)\\)\uac00 \\(\\tau_X\\)\uc5d0 \uc18d\ud558\uba74 \\(F\\)\ub97c <span class=\"defined\">\uc5f0\uc18d<\/span>(continuous)\uc774\ub77c\uace0 \ud55c\ub2e4. \uc774\ub807\uac8c \uc5f0\uc18d\uc131\uc740 \u03b5\uc640 \u03b4\ub97c \uc9c1\uc811 \uc5b8\uae09\ud558\uc9c0 \uc54a\uace0 \u2018\uc5f4\ub9b0\uc9d1\ud569\uc758 \uc6d0\uc0c1\uc740 \uc5f4\ub9b0\uc9d1\ud569\uc774\ub2e4\u2019\ub77c\ub294 \uc870\uac74\uc73c\ub85c \ud45c\ud604\ub41c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<h4>\ub450 \uc815\uc758\ub97c \uc787\ub294 \ub2e4\ub9ac<\/h4>\n<p>\uac70\ub9ac\uacf5\uac04 \\((X,d)\\)\uc5d0\uc11c \uc810 \\(x\\in X\\)\uc640 \\(r>0\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\nB(x,r)=\\{y\\in X:d(x,y)<r\\}\n\\]\n\ub97c <span class=\"defined\">\uc5f4\ub9b0\uacf5<\/span>(open ball)\uc774\ub77c\uace0 \ud558\uc790. \ubd80\ubd84\uc9d1\ud569 \\(U\\subseteq X\\)\uac00 \uc5f4\ub9b0\ub2e4\ub294 \uac83\uc744, \ubaa8\ub4e0 \\(x\\in U\\)\uc5d0 \ub300\ud558\uc5ec \\(B(x,r)\\subseteq U\\)\uc778 \\(r>0\\)\uac00 \uc874\uc7ac\ud558\ub294 \uac83\uc73c\ub85c \uc815\uc758\ud55c\ub2e4. \uc774\ub807\uac8c \uc5bb\uc740 \uc5f4\ub9b0\uc9d1\ud569\ub4e4\uc758 \uc871\uc740 \uc704\uc0c1\uc758 \uc138 \uacf5\ub9ac\ub97c \ub9cc\uc871\ud558\uba70, \uc774\ub97c \uac70\ub9ac \\(d\\)\uac00 <span class=\"defined\">\uc720\ub3c4\ud558\ub294 \uc704\uc0c1<\/span>(induced topology)\uc774\ub77c\uace0 \ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<p>[\uc5f4\ub9b0\uacf5 \uc790\uccb4\ub3c4 \uc5f4\ub9b0\uc9d1\ud569\uc774\ub2e4. \\(y\\in B(x,r)\\)\ub77c\uba74 \\(r&#8217;=r-d(x,y)>0\\)\ub85c \ub458 \uc218 \uc788\ub2e4. \\(z\\in B(y,r&#8217;)\\)\uc77c \ub54c \uc0bc\uac01\ubd80\ub4f1\uc2dd\uc73c\ub85c<br \/>\n\\[<br \/>\nd(x,z)\\le d(x,y)+d(y,z)<d(x,y)+r'=r\n\\]\n\uc774\ubbc0\ub85c \\(B(y,r')\\subseteq B(x,r)\\)\uc774\ub2e4.]<\/p>\n<div class=\"box theorem\">\n<p><span class=\"theorem\">\uc815\ub9ac: \uc5f0\uc18d\uc131\uc758 \ub450 \uc815\uc758\uc758 \ub3d9\uce58 \uc131\uc9c8<\/span><br \/>\n\ub450 \uac70\ub9ac\uacf5\uac04 \\((X,d_X)\\), \\((Y,d_Y)\\)\uc640 \ud568\uc218 \\(F:X\\to Y\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c \ub450 \uc870\uac74\uc740 \ub3d9\uce58\uc774\ub2e4.<\/p>\n<ul>\n<li><strong>\u03b5-\u03b4 \uc5f0\uc18d\uc131:<\/strong> \ubaa8\ub4e0 \\(x_0\\in X\\)\uc640 \ubaa8\ub4e0 \\(\\varepsilon>0\\)\uc5d0 \ub300\ud558\uc5ec \uc5b4\ub5a4 \\(\\delta>0\\)\uac00 \uc874\uc7ac\ud558\uc5ec, \\(d_X(x,x_0)<\\delta\\)\uc774\uba74 \\(d_Y(F(x),F(x_0))<\\varepsilon\\)\uc774\ub2e4.<\/li>\n<li><strong>\uc704\uc0c1\uc801 \uc5f0\uc18d\uc131:<\/strong> \\(Y\\)\uc758 \ubaa8\ub4e0 \uc5f4\ub9b0\uc9d1\ud569 \\(V\\)\uc5d0 \ub300\ud558\uc5ec \\(F^{-1}(V)\\)\ub294 \\(X\\)\uc5d0\uc11c \uc5f4\ub9b0\uc9d1\ud569\uc774\ub2e4. \uc5ec\uae30\uc11c \ub450 \uc704\uc0c1\uc740 \uac01\uac01 \\(d_X,d_Y\\)\uac00 \uc720\ub3c4\ud55c\ub2e4.<\/li>\n<\/ul>\n<\/div>\n<p>\uba3c\uc800 \\(F\\)\uac00 \u03b5-\u03b4 \uc5f0\uc18d\uc774\uace0 \\(V\\subseteq Y\\)\uac00 \uc5f4\ub9b0\uc9d1\ud569\uc774\ub77c\uace0 \ud558\uc790. \uc784\uc758\uc758 \\(x\\in F^{-1}(V)\\)\uc5d0 \ub300\ud558\uc5ec \\(F(x)\\in V\\)\uc774\ubbc0\ub85c, \uc5b4\ub5a4 \\(\\varepsilon>0\\)\uac00 \uc874\uc7ac\ud558\uc5ec \\(B(F(x),\\varepsilon)\\subseteq V\\)\uc774\ub2e4. \u03b5-\u03b4 \uc5f0\uc18d\uc131\uc5d0 \ub530\ub77c \uc5b4\ub5a4 \\(\\delta>0\\)\uac00 \uc874\uc7ac\ud558\uc5ec<br \/>\n\\[<br \/>\nF(B(x,\\delta))\\subseteq B(F(x),\\varepsilon)\\subseteq V<br \/>\n\\]<br \/>\n\uac00 \ub41c\ub2e4. \ub530\ub77c\uc11c \\(B(x,\\delta)\\subseteq F^{-1}(V)\\)\uc774\ub2e4. \uc774\ub294 \\(F^{-1}(V)\\)\uc758 \ubaa8\ub4e0 \uc810\uc774 \uadf8 \uc548\uc5d0 \ud3ec\ud568\ub418\ub294 \uc5f4\ub9b0\uacf5\uc744 \uac00\uc9c0\ubbc0\ub85c \\(F^{-1}(V)\\)\uac00 \uc5f4\ub824 \uc788\uc74c\uc744 \ub73b\ud55c\ub2e4.<\/p>\n<p>\ubc18\ub300\ub85c \ubaa8\ub4e0 \uc5f4\ub9b0\uc9d1\ud569\uc758 \uc6d0\uc0c1\uc774 \uc5f4\ub824 \uc788\ub2e4\uace0 \ud558\uc790. \\(x_0\\in X\\)\uc640 \\(\\varepsilon>0\\)\ub97c \uc784\uc758\ub85c \uc7a1\uc73c\uba74 \\(B(F(x_0),\\varepsilon)\\)\ub294 \\(Y\\)\uc758 \uc5f4\ub9b0\uc9d1\ud569\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c<br \/>\n\\[<br \/>\nF^{-1}(B(F(x_0),\\varepsilon))<br \/>\n\\]<br \/>\n\ub294 \\(x_0\\)\ub97c \ud3ec\ud568\ud558\ub294 \\(X\\)\uc758 \uc5f4\ub9b0\uc9d1\ud569\uc774\ub2e4. \ub530\ub77c\uc11c \uc5b4\ub5a4 \\(\\delta>0\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\nB(x_0,\\delta)\\subseteq F^{-1}(B(F(x_0),\\varepsilon))<br \/>\n\\]<br \/>\n\uc774\ub2e4. \uc989 \\(d_X(x,x_0)<\\delta\\)\uc774\uba74 \\(d_Y(F(x),F(x_0))<\\varepsilon\\)\uc774\ubbc0\ub85c \\(F\\)\ub294 \u03b5-\u03b4 \uc5f0\uc18d\uc774\ub2e4. \uc774\ub85c\uc368 \ub450 \uc815\uc758\uac00 \ub3d9\uce58\uc784\uc774 \uc99d\uba85\ub418\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<p><!--\n\n\n<p>\ub530\ub77c\uc11c \uc704\uc0c1\uc801 \uc5f0\uc18d\uc131\uc740 \uac70\ub9ac\uacf5\uac04\uc5d0\uc11c \uae30\uc874\uc758 \u03b5-\u03b4 \uc5f0\uc18d\uc131\uacfc \ucda9\ub3cc\ud558\ub294 \uc0c8 \uac1c\ub150\uc774 \uc544\ub2c8\ub2e4.\uac70\ub9ac\uacf5\uac04\uc5d0\uc11c\ub294 \uac19\uc740 \uac1c\ub150\uc744 \ub354 \uc77c\ubc18\uc801\uc778 \uc5b8\uc5b4\ub85c \ub2e4\uc2dc \ud45c\ud604\ud55c \uac83\uc774\uba70, \ub3d9\uc2dc\uc5d0 \uac70\ub9ac\ub85c\ubd80\ud130 \ub098\uc624\uc9c0 \uc54a\ub294 \uc704\uc0c1\uacf5\uac04\uc5d0\ub3c4 \uc801\uc6a9\ud560 \uc218 \uc788\ub294 \ud655\uc7a5\uc774\ub2e4.<\/p>\n\n\n--><\/p>\n<h4>\uc815\ub9ac\uac00 \uc815\uc758\uac00 \ub418\ub2e4: \ucef4\ud329\ud2b8\uc131<\/h4>\n<p><span class=\"defined\">\ud558\uc774\ub124\u2013\ubcf4\ub810 \uc815\ub9ac<\/span>(Heine\u2013Borel theorem)\ub294 \uc720\ud074\ub9ac\ub4dc \uacf5\uac04 \\(\\mathbb R^n\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(K\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c \ub450 \uc870\uac74\uc774 \ub3d9\uce58\ub77c\uace0 \ub9d0\ud55c\ub2e4.<\/p>\n<ul>\n<li>\\(K\\)\ub294 \ub2eb\ud600 \uc788\uace0 \uc720\uacc4\uc774\ub2e4.<\/li>\n<li>\\(K\\)\uc758 \ubaa8\ub4e0 \uc5f4\ub9b0\ub36e\uac1c\ub294 \uc720\ud55c \ubd80\ubd84\ub36e\uac1c\ub97c \uac16\ub294\ub2e4.<\/li>\n<\/ul>\n<p>\uc5ec\uae30\uc11c \uc5f4\ub9b0\ub36e\uac1c\ub294 \\(K\\subseteq\\bigcup_{\\alpha\\in A}U_\\alpha\\)\ub97c \ub9cc\uc871\ud558\ub294 \uc5f4\ub9b0\uc9d1\ud569\ub4e4\uc758 \uc871 \\(\\{U_\\alpha\\}_{\\alpha\\in A}\\)\uc774\uace0, \uc720\ud55c \ubd80\ubd84\ub36e\uac1c\ub294 \uadf8 \uac00\uc6b4\ub370 \uc720\ud55c \uac1c\ub9cc \uace8\ub77c\ub3c4 \\(K\\)\ub97c \ub36e\ub294 \uacbd\uc6b0\ub97c \ub9d0\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<p>[<!-- \ud558\uc774\ub124\u2013\ubcf4\ub810 \uc815\ub9ac\uc758 \uc5ed\uc0ac\ub294 \uc774\ub984\ubcf4\ub2e4 \ubcf5\uc7a1\ud558\ub2e4. -->\uc774 \uc815\ub9ac\uc758 \uc774\ub984\uc5d0\ub294 \ud558\uc774\ub124\uc640 \ubcf4\ub810 \ub450 \uc0ac\ub78c\ub9cc \ub0a8\uc558\uc9c0\ub9cc, \uc0ac\uc2e4 \uadf8 \uc774\uba74\uc5d0\ub294 \ub354 \ub9ce\uc740 \uc218\ud559\uc790\uc758 \uae30\uc5ec\uac00 \uc5bd\ud600 \uc788\ub2e4. 19\uc138\uae30 \uc911\uc5fd\uc758 \uade0\ub4f1\uc5f0\uc18d\uc131 \ub17c\uc99d\uc5d0\ub294 \uc774\ubbf8 \uc720\ud55c \ub36e\uac1c\ub97c \uc120\ud0dd\ud558\ub294 \uc0dd\uac01\uc774 \ub098\ud0c0\ub0ac\uace0, \ubcf4\ub810\uc740 1895\ub144 \ub2eb\ud78c\uad6c\uac04\uc758 \uac00\uc0b0 \uc5f4\ub9b0\uad6c\uac04 \ub36e\uac1c\uc5d0 \uad00\ud55c \ud615\ud0dc\ub97c \uc99d\uba85\ud588\ub2e4. \uac19\uc740 \ud574 \ucfe0\uc7c1(Pierre Cousin)\uc740 \uc784\uc758\ub85c \uc8fc\uc5b4\uc9c4 \uad6d\uc18c \uadfc\ubc29\uc5d0\uc11c \uc720\ud55c \ubd84\ud560\uc744 \uc5bb\ub294 \ub354 \uc77c\ubc18\uc801\uc778 \ubcf4\uc870\uc815\ub9ac\ub97c \ubc1c\ud45c\ud588\uc73c\uba70, \uc774\ud6c4 \uc5ec\ub7ec \uc218\ud559\uc790\uac00 \uc624\ub298\ub0a0\uc758 \uc784\uc758 \uc5f4\ub9b0\ub36e\uac1c \ud615\uc2dd\uc744 \uc815\ub9ac\ud588\ub2e4. <!-- \uc774\ub97c \ud558\uc774\ub124\u00b7\ubcf4\ub810\u00b7\ub974\ubca0\uadf8 \uc138 \uc0ac\ub78c\uc758 \ub2e8\uc21c\ud55c \uc9c1\uc120\uc801 \uacc4\ubcf4\ub85c\ub9cc \uc124\uba85\ud558\ub294 \uac83\uc740 \uc815\ud655\ud558\uc9c0 \uc54a\ub2e4.<a class=\"math-abs-series-ref\" title=\"Andre, N. R., Engdahl, S. M., &amp; Parker, A. E. (2013). \u201cAn Analysis of the First Proofs of the Heine\u2013Borel Theorem.\u201d Convergence.\" href=\"#ref-AndreEtAl2013\">[AndreEtAl2013]<\/a><a class=\"math-abs-series-ref\" title=\"Raman-Sundstr\u00f6m, M. (2015). \u201cA Pedagogical History of Compactness.\u201d The American Mathematical Monthly, 122(7), 619\u2013635. \uacf5\uac1c \uc6d0\uace0: arXiv:1006.4131.\" href=\"#ref-RamanSundstrom2015\">[RamanSundstrom2015]<\/a>] --><\/p>\n<p>\uc774\uc81c \uc784\uc758\uc758 \uc704\uc0c1\uacf5\uac04 \\(X\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(K\\)\uc5d0 \ubd80\ubd84\uacf5\uac04 \uc704\uc0c1\uc744 \uc8fc\uc790. \\(K\\)\uc758 \ubaa8\ub4e0 \uc5f4\ub9b0\ub36e\uac1c\uac00 \uc720\ud55c \ubd80\ubd84\ub36e\uac1c\ub97c \uac00\uc9c0\uba74 \\(K\\)\ub97c <span class=\"defined\">\ucef4\ud329\ud2b8<\/span>(compact)\ud558\ub2e4\uace0 \uc815\uc758\ud55c\ub2e4. \uc774 \uc815\uc758\ub97c \uc0ac\uc6a9\ud558\uba74 \ud558\uc774\ub124\u2013\ubcf4\ub810 \uc815\ub9ac\ub294 \u201c\\(\\mathbb R^n\\)\uc5d0\uc11c\ub294 \ucef4\ud329\ud2b8\ud568\uacfc \ub2eb\ud788\uace0 \uc720\uacc4\uc784\uc774 \ub3d9\uce58\uc774\ub2e4\u201d\ub77c\ub294 \uc815\ub9ac\uac00 \ub41c\ub2e4. \uc5f4\ub9b0\ub36e\uac1c \uc870\uac74\uc740 \uac70\ub9ac\ub098 \ub178\ub984\uc744 \uc5b8\uae09\ud558\uc9c0 \uc54a\uc73c\ubbc0\ub85c \ubaa8\ub4e0 \uc704\uc0c1\uacf5\uac04\uc5d0\uc11c \uc758\ubbf8\ub97c \uac16\ub294\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<p>\ub610 \ub2e4\ub978 \uc77c\ubc18\ud654\ub294 \uc218\uc5f4\uc5d0\uc11c \ucd9c\ubc1c\ud55c\ub2e4. \uacf5\uac04 \\(K\\)\uc758 \ubaa8\ub4e0 \uc218\uc5f4\uc774 \\(K\\)\uc758 \ud55c \uc810\uc73c\ub85c \uc218\ub834\ud558\ub294 \ubd80\ubd84\uc218\uc5f4\uc744 \uac00\uc9c0\uba74 \\(K\\)\ub97c <span class=\"defined\">\uc810\uc5f4 \ucef4\ud329\ud2b8<\/span>(sequentially compact)\ud558\ub2e4\uace0 \ud55c\ub2e4. \ubaa8\ub4e0 \uac70\ub9ac\uacf5\uac04\uc5d0\uc11c\ub294 \ucef4\ud329\ud2b8\uc131\uacfc \uc810\uc5f4 \ucef4\ud329\ud2b8\uc131\uc774 \uc11c\ub85c \ub3d9\uce58\uc774\ub2e4.<\/p>\n<p>[\uac70\ub9ac\uacf5\uac04\uc5d0\uc11c \ub450 \uc870\uac74\uc774 \ub3d9\uce58\ub77c\ub294 \uc99d\uba85\uc740 \ud45c\uc900 \uc704\uc0c1\uc218\ud559 \uc815\ub9ac\uc774\ub2e4. \ud55c \ubc29\ud5a5\uc5d0\uc11c\ub294 \ucef4\ud329\ud2b8\uc131\uc774 \uac01 \\(\\varepsilon\\)-\ud06c\uae30\uc758 \uacf5\ub4e4\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc720\ud55c \ub36e\uac1c\ub97c \uc81c\uacf5\ud55c\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc774\uc6a9\ud574 \uc218\uc5f4\uc758 \ucf54\uc2dc \ubd80\ubd84\uc218\uc5f4\uc744 \ub9cc\ub4e4\uace0, \ub2e4\ub978 \ubc29\ud5a5\uc5d0\uc11c\ub294 \uc810\uc5f4 \ucef4\ud329\ud2b8\uc131\uc744 \uc774\uc6a9\ud574 \uc5f4\ub9b0\ub36e\uac1c\uc5d0 \ub974\ubca0\uadf8 \uc218\uac00 \uc874\uc7ac\ud568\uc744 \ubcf4\uc778 \ub4a4 \uc720\ud55c \ubd80\ubd84\ub36e\uac1c\ub97c \uc5bb\uc744 \uc218 \uc788\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a>]<\/p>\n<p>\uadf8\ub7ec\ub098 \u201c\ub2eb\ud788\uace0 \uc720\uacc4\uc774\uba74 \ucef4\ud329\ud2b8\ud558\ub2e4\u201d\ub294 \uba85\uc81c\ub294 \uc77c\ubc18 \uac70\ub9ac\uacf5\uac04\uc774\ub098 \ubb34\ud55c\ucc28\uc6d0 \ub178\ub984\uacf5\uac04\uc5d0\uc11c\ub294 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294\ub2e4. \ud2b9\ud788 \ubb34\ud55c\ucc28\uc6d0 \ub178\ub984\uacf5\uac04\uc758 \ub2eb\ud78c \ub2e8\uc704\uacf5<br \/>\n\\[<br \/>\n\\overline B(0,1)=\\{x:\\|x\\|\\le1\\}<br \/>\n\\]<br \/>\n\uc740 \ub2eb\ud788\uace0 \uc720\uacc4\uc774\uc9c0\ub9cc \ucef4\ud329\ud2b8\ud558\uc9c0 \uc54a\ub2e4. \ub9ac\uc2a4 \ubcf4\uc870\uc815\ub9ac\ub97c \ubc18\ubcf5\ud574 \uc801\uc6a9\ud558\uba74 \ub2e8\uc704\uacf5 \uc548\uc5d0\uc11c \uc11c\ub85c \uc77c\uc815\ud55c \uc591 \uc774\uc0c1 \ub5a8\uc5b4\uc9c4 \uc218\uc5f4\uc744 \ub9cc\ub4e4 \uc218 \uc788\uace0, \uc774 \uc218\uc5f4\uc740 \uc218\ub834\ud558\ub294 \ubd80\ubd84\uc218\uc5f4\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4.<a class=\"math-abs-series-ref\" title=\"Hunter, J. K., &amp; Nachtergaele, B. (2001). Applied Analysis. World Scientific.\" href=\"#ref-HunterNachtergaele2001\">[HunterNachtergaele2001]<\/a> <!-- \uadf8\ub807\ub2e4\uace0 \ubb34\ud55c\ucc28\uc6d0 \uacf5\uac04\uc758 \ubaa8\ub4e0 \ub2eb\ud78c \uc720\uacc4\uc9d1\ud569\uc774 \ube44\ucef4\ud329\ud2b8\ud55c \uac83\uc740 \uc544\ub2c8\ub2e4. \uc720\ud55c\uc9d1\ud569\uc774\ub098 \uc218\ub834\uc218\uc5f4\uacfc \uadf8 \uadf9\ud55c\uc758 \ud569\uc9d1\ud569\ucc98\ub7fc \ucef4\ud329\ud2b8\ud55c \uc9d1\ud569\ub3c4 \uc874\uc7ac\ud55c\ub2e4. \uc815\ud655\ud55c \uacb0\ub860\uc740 \u2018\ub2eb\ud798\uacfc \uc720\uacc4\uc131\ub9cc\uc73c\ub85c\ub294 \ucef4\ud329\ud2b8\uc131\uc744 \ubcf4\uc7a5\ud558\uc9c0 \uc54a\ub294\ub2e4\u2019\ub294 \uac83\uc774\ub2e4. --><\/p>\n<p>\uc5f4\ub9b0\ub36e\uac1c\uc5d0 \uc758\ud55c \ucef4\ud329\ud2b8\uc131\uc740 20\uc138\uae30 \ucd08 \uc5ec\ub7ec \uacbd\uc7c1 \uac1c\ub150 \uac00\uc6b4\ub370 \uc815\ub9ac\ub418\uc5c8\ub2e4. \uc54c\ub809\uc0b0\ub4dc\ub85c\ud504(Pavel Alexandroff)\uc640 \uc6b0\ub9ac\uc190(Pavel Urysohn)\uc740 1923\ub144 \ub17c\ubb38\uc5d0\uc11c \uc5f4\ub9b0\ub36e\uac1c\uc758 \uc720\ud55c \ubd80\ubd84\ub36e\uac1c \uc131\uc9c8\uc744 \uc77c\ubc18 \uacf5\uac04\uc758 \ud575\uc2ec \uc870\uac74\uc73c\ub85c \uc81c\uc2dc\ud558\uace0 \u2018\uc30d\ucf64\ud329\ud2b8(bicompact)\u2019\ub77c\ub294 \ub9d0\uc744 \uc0ac\uc6a9\ud588\ub2e4. \uc624\ub298\ub0a0\uc5d0\ub294 \ub300\uccb4\ub85c \uc774 \uc5f4\ub9b0\ub36e\uac1c \uc870\uac74 \uc790\uccb4\ub97c \ucef4\ud329\ud2b8\uc131\uc774\ub77c \ubd80\ub974\uba70, \ud558\uc6b0\uc2a4\ub3c4\ub974\ud504 \uc870\uac74\uc774 \ud544\uc694\ud558\uba74 \u2018\ucef4\ud329\ud2b8 \ud558\uc6b0\uc2a4\ub3c4\ub974\ud504\u2019\ub77c\uace0 \ub530\ub85c \uba85\uc2dc\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Raman-Sundstr\u00f6m, M. (2015). \u201cA Pedagogical History of Compactness.\u201d The American Mathematical Monthly, 122(7), 619\u2013635. \uacf5\uac1c \uc6d0\uace0: arXiv:1006.4131.\" href=\"#ref-RamanSundstrom2015\">[RamanSundstrom2015]<\/a><\/p>\n<p>[\ucef4\ud329\ud2b8\uc131\uc774\ub77c\ub294 \ub0af\uc120 \uac1c\ub150\uc774 \uc624\ub298\ub0a0\uc758 \uc138\ub828\ub41c \ubaa8\uc2b5\uc744 \uac16\ucd94\uae30\uae4c\uc9c0\ub294 \uaf64 \uc624\ub79c \uc2dc\uac04\uc774 \uac78\ub838\ub2e4. \ud504\ub808\uc170\uc758 1906\ub144 \uc5f0\uad6c\uc5d0\ub294 \uc218\uc5f4\uacfc \uadf9\ud55c\uc810\uc5d0 \uae30\ucd08\ud55c \uc5ec\ub7ec \uc870\uac74\uc774 \uc788\uc5c8\uace0, \ud558\uc6b0\uc2a4\ub3c4\ub974\ud504\uc758 \uc815\uc758\ub3c4 \uc624\ub298\ub0a0\uc758 \uc5f4\ub9b0\ub36e\uac1c \ucef4\ud329\ud2b8\uc131\uacfc \uac19\uc9c0 \uc54a\uc558\ub2e4. \uc54c\ub809\uc0b0\ub4dc\ub85c\ud504\uc640 \uc6b0\ub9ac\uc190\uc758 1923\ub144 \uc791\uc5c5\uc740 \uc77c\ubc18 \uc704\uc0c1\uacf5\uac04\uc5d0\uc11c \uc5f4\ub9b0\ub36e\uac1c \uc870\uac74\uc744 \uc804\uba74\uc5d0 \ub193\uc740 \uc911\uc694\ud55c \ub2e8\uacc4\uc600\ub2e4. \uc624\ub298\ub0a0 \ub9ce\uc740 \uc77c\ubc18\uc704\uc0c1 \uad50\uc7ac\ub294 \uc720\ud55c \ubd80\ubd84\ub36e\uac1c \uc870\uac74\ub9cc\uc744 \u2018\ucef4\ud329\ud2b8\u2019\ub77c\uace0 \ubd80\ub974\uc9c0\ub9cc, \ubd80\ub974\ubc14\ud0a4 \uacc4\uc5f4\uacfc \ub300\uc218\uae30\ud558 \ubb38\ud5cc\uc5d0\uc11c\ub294 \uc774\ub97c \u2018\uc900\ucef4\ud329\ud2b8(quasi-compact)\u2019\ub77c\uace0 \ud558\uace0 \ud558\uc6b0\uc2a4\ub3c4\ub974\ud504 \uc870\uac74\uae4c\uc9c0 \ub9cc\uc871\ud560 \ub54c \u2018\ucef4\ud329\ud2b8\u2019\ub77c\uace0 \ubd80\ub974\uae30\ub3c4 \ud55c\ub2e4.<!-- \ubb38\ud5cc\uc758 \uad00\ub840\ub97c \ud655\uc778\ud574\uc57c \ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Fr\u00e9chet, M. (1906). \u201cSur quelques points du calcul fonctionnel.\u201d Rendiconti del Circolo Matematico di Palermo, 22, 1\u201372.\" href=\"#ref-Frechet1906\">[Frechet1906]<\/a><a class=\"math-abs-series-ref\" title=\"Raman-Sundstr\u00f6m, M. (2015). \u201cA Pedagogical History of Compactness.\u201d The American Mathematical Monthly, 122(7), 619\u2013635. \uacf5\uac1c \uc6d0\uace0: arXiv:1006.4131.\" href=\"#ref-RamanSundstrom2015\">[RamanSundstrom2015]<\/a> -->]<\/p>\n<p>\uc5f4\ub9b0\ub36e\uac1c \uc815\uc758\uc758 \uac15\uc810\uc740 \uacf1\uacf5\uac04\uc5d0\uc11c \ud2b9\ud788 \uc120\uba85\ud558\ub2e4. <span class=\"defined\">\ud2f0\ud638\ub178\ud504 \uc815\ub9ac<\/span>(Tychonoff\u2019s theorem)\ub294 \uc784\uc758\uc758 \uc9c0\ud45c\uc9d1\ud569 \\(I\\)\uc640 \ucef4\ud329\ud2b8 \uacf5\uac04\ub4e4 \\(\\{X_i\\}_{i\\in I}\\)\uc5d0 \ub300\ud558\uc5ec, \uacf1\uc704\uc0c1\uc744 \uc900 \uacf1\uacf5\uac04<br \/>\n\\[<br \/>\n\\prod_{i\\in I}X_i<br \/>\n\\]<br \/>\n\uac00 \ucef4\ud329\ud2b8\ud558\ub2e4\uace0 \ub9d0\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Tychonoff, A. (1935). \u201c\u00dcber einen Funktionenraum.\u201d Mathematische Annalen, 111, 762\u2013766. \uc6d0\ubb38: EuDML.\" href=\"#ref-Tychonoff1935\">[Tychonoff1935]<\/a><\/p>\n<p>[\ud2f0\ud638\ub178\ud504\ub294 1930\ub144\uc5d0 \ub2eb\ud78c \ub2e8\uc704\uad6c\uac04\uc758 \uc784\uc758 \uac70\ub4ed\uc81c\uacf1\uc5d0 \ud574\ub2f9\ud558\ub294 \uacbd\uc6b0\ub97c \ub2e4\ub8e8\uc5c8\uace0, 1935\ub144 \u300c\ud568\uc218\uacf5\uac04\uc5d0 \uad00\ud558\uc5ec\u300d\uc5d0\uc11c \uc77c\ubc18 \uacf1\uc815\ub9ac\ub97c \ubc1c\ud45c\ud588\ub2e4. \ubaa8\ub4e0 \ucef4\ud329\ud2b8 \uacf5\uac04\uc758 \uc784\uc758 \uacf1\uc5d0 \uad00\ud55c \uc815\ub9ac\ub294 \ud1b5\uc0c1\uc801\uc778 \uc9d1\ud569\ub860 ZF \uc704\uc5d0\uc11c \uc120\ud0dd\uacf5\ub9ac\uc640 \ub3d9\uce58\uc774\uba70, \uc5ed\ubc29\ud5a5\uc740 \ucf08\ub9ac(John L. Kelley)\uac00 1950\ub144\uc5d0 \uc99d\uba85\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"Raman-Sundstr\u00f6m, M. (2015). \u201cA Pedagogical History of Compactness.\u201d The American Mathematical Monthly, 122(7), 619\u2013635. \uacf5\uac1c \uc6d0\uace0: arXiv:1006.4131.\" href=\"#ref-RamanSundstrom2015\">[RamanSundstrom2015]<\/a><a class=\"math-abs-series-ref\" title=\"Tychonoff, A. (1935). \u201c\u00dcber einen Funktionenraum.\u201d Mathematische Annalen, 111, 762\u2013766. \uc6d0\ubb38: EuDML.\" href=\"#ref-Tychonoff1935\">[Tychonoff1935]<\/a><a class=\"math-abs-series-ref\" title=\"Kelley, J. L. (1950). \u201cThe Tychonoff Product Theorem Implies the Axiom of Choice.\u201d Fundamenta Mathematicae, 37(1), 75\u201376. EuDML.\" href=\"#ref-Kelley1950\">[Kelley1950]<\/a>]<\/p>\n<p>\ubc18\uba74 \uc810\uc5f4 \ucef4\ud329\ud2b8\uc131\uc740 \uc784\uc758\uc758 \uacf1\uc5d0\uc11c \ubcf4\uc874\ub418\uc9c0 \uc54a\ub294\ub2e4. \uac01 \uc778\uc790\uac00 \uc810\uc5f4 \ucef4\ud329\ud2b8\ud558\ub354\ub77c\ub3c4 \ube44\uac00\uc0b0 \uacf1\uc740 \uc810\uc5f4 \ucef4\ud329\ud2b8\ud558\uc9c0 \uc54a\uc744 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c \uc77c\ubc18 \uc704\uc0c1\uc218\ud559\uc5d0\uc11c\ub294 \uc218\uc5f4\ub9cc\uc73c\ub85c \ud3ec\ucc29\ub418\uc9c0 \uc54a\ub294 \ucef4\ud329\ud2b8 \ud604\uc0c1\uc744 \uc5f4\ub9b0\ub36e\uac1c, \ub610\ub294 \uadf8\uc640 \ub3d9\uce58\uc778 \ub9dd(net)\u00b7\ud544\ud130\uc758 \uc5b8\uc5b4\ub85c \ub2e4\ub8ec\ub2e4.<a class=\"math-abs-series-ref\" title=\"Engelking, R. (1989). General Topology (revised and completed ed.). Sigma Series in Pure Mathematics, 6. Heldermann Verlag. \ucd9c\ud310\uc0ac \uc11c\uc9c0.\" href=\"#ref-Engelking1989\">[Engelking1989]<\/a><\/p>\n<p>[\ud45c\uc900\uc801\uc778 \ubc18\ub840\ub294 \uc774\uc0b0\uc704\uc0c1\uc744 \uc900 \ub450 \uc810 \uacf5\uac04 \\(2=\\{0,1\\}\\)\uc758 \\(\\mathcal P(\\mathbb N)\\)-\uac1c \uacf1 \\(2^{\\mathcal P(\\mathbb N)}\\)\uc774\ub2e4. \uac01 \uc778\uc790\ub294 \uc720\ud55c\ud558\ubbc0\ub85c \ucef4\ud329\ud2b8\ud558\uace0 \uc810\uc5f4 \ucef4\ud329\ud2b8\ud558\uba70, \uc804\uccb4 \uacf1\uc740 \ud2f0\ud638\ub178\ud504 \uc815\ub9ac\uc5d0 \uc758\ud574 \ucef4\ud329\ud2b8\ud558\ub2e4. \uadf8\ub7ec\ub098 \\(n\\in\\mathbb N\\)\uc5d0 \ub300\ud558\uc5ec \\(x_n(A)=1\\Longleftrightarrow n\\in A\\)\ub85c \uc218\uc5f4 \\((x_n)\\)\uc744 \uc815\uc758\ud558\uc790. \uc784\uc758\uc758 \ubd80\ubd84\uc218\uc5f4 \\((x_{n_k})\\)\uc5d0 \ub300\ud574 \\(A=\\{n_{2k}:k\\in\\mathbb N\\}\\)\ub77c\ub294 \uc88c\ud45c\ub97c \ud0dd\ud558\uba74 \\(x_{n_k}(A)\\)\uac00 \\(0\\)\uacfc \\(1\\)\uc744 \ubc88\uac08\uc544 \uac00\uc9c0\ubbc0\ub85c \uadf8 \ubd80\ubd84\uc218\uc5f4\uc740 \uadf8 \uc88c\ud45c\uc5d0\uc11c \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4. \ub530\ub77c\uc11c \uc218\ub834\ud558\ub294 \ubd80\ubd84\uc218\uc5f4\uc774 \uc5c6\ub2e4. \\(|\\mathcal P(\\mathbb N)|=|[0,1]|\\)\uc774\ubbc0\ub85c \uc6d0\ubb38\uc5d0 \ub4f1\uc7a5\ud55c \\(2^{[0,1]}\\)\ub3c4 \uac19\uc740 \ubc18\ub840\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Engelking, R. (1989). General Topology (revised and completed ed.). Sigma Series in Pure Mathematics, 6. Heldermann Verlag. \ucd9c\ud310\uc0ac \uc11c\uc9c0.\" href=\"#ref-Engelking1989\">[Engelking1989]<\/a>]<\/p>\n<p>\ube44\uc2b7\ud55c \uad00\uc810\uc740 <span class=\"defined\">\uc5f0\uacb0\uc131<\/span>(connectedness)\uc5d0\ub3c4 \uc801\uc6a9\ub41c\ub2e4. \uc704\uc0c1\uacf5\uac04 \\(X\\)\ub97c \uc11c\ub85c\uc18c\uc774\uace0 \uacf5\uc9d1\ud569\uc774 \uc544\ub2cc \ub450 \uc5f4\ub9b0\uc9d1\ud569\uc758 \ud569\uc9d1\ud569\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc5c6\uc744 \ub54c \\(X\\)\uac00 \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4\uace0 \ud55c\ub2e4. \uc2e4\uc218\uc758 \uad6c\uac04\uc740 \uc5f0\uacb0\ub418\uc5b4 \uc788\uace0, \uc5f0\uacb0\uacf5\uac04\uc758 \uc5f0\uc18d\uc0c1\uc740 \ub2e4\uc2dc \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4. \uc2e4\uc218\uac12 \uc5f0\uc18d\ud568\uc218\uc5d0 \uc774 \uc815\ub9ac\ub97c \uc801\uc6a9\ud558\uba74 \uc0ac\uc787\uac12 \uc815\ub9ac\ub97c \uc5bb\ub294\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a> \uc774 \uc5f0\uc7ac\uc758 \uad00\uc810\uc5d0\uc11c \ubcf4\uba74 \ud558\uc774\ub124\u2013\ubcf4\ub810 \uc815\ub9ac\uc640 \uc0ac\uc787\uac12 \uc815\ub9ac\uc758 \ubc30\ud6c4\uc5d0 \uc788\ub358 \uc131\uc9c8\uc774 \uac01\uac01 \ucef4\ud329\ud2b8\uc131\uacfc \uc5f0\uacb0\uc131\uc774\ub77c\ub294 \uc77c\ubc18 \uac1c\ub150\uc73c\ub85c \ubd84\ub9ac\ub41c \uc148\uc774\ub2e4. <!-- \ub2e4\ub9cc \uc774\ub294 \ud558\ub098\uc758 \uc815\ub9ac \ubb38\uc7a5\uc744 \uadf8\ub300\ub85c \uc815\uc758\ub85c \uc62e\uae34 \ub2e8\uc77c\ud55c \uc5ed\uc0ac\uc801 \uc0ac\uac74\uc774\ub77c\uae30\ubcf4\ub2e4, \uc5ec\ub7ec \ub3d9\uce58 \uc870\uac74 \uac00\uc6b4\ub370 \ub354 \ub113\uc740 \uacf5\uac04\uc5d0\uc11c\ub3c4 \uc548\uc815\uc801\uc73c\ub85c \uc791\ub3d9\ud558\ub294 \uc870\uac74\uc744 \uace8\ub77c\ub0b8 \uae34 \ubc1c\uc804 \uacfc\uc815\uc774\uc5c8\ub2e4. --><\/p>\n<h4>\uac70\ub9ac\ub85c \ud45c\ud604\ub418\uc9c0 \uc54a\ub294 \uc790\uc5f0\uc2a4\ub7ec\uc6b4 \uc704\uc0c1<\/h4>\n<p>\uac70\ub9ac\uacf5\uac04\ub9cc\uc73c\ub85c \ucda9\ubd84\ud558\uc9c0 \uc54a\ub2e4\ub294 \uc0ac\uc2e4\uc744 \ubcf4\uc5ec \uc8fc\ub294 \ub300\ud45c\uc801\uc778 \uc608\uac00 \ube44\uac00\uc0b0 \uc9d1\ud569 \uc704\uc758 \ud568\uc218\uacf5\uac04\uc774\ub2e4. \uc9d1\ud569 \\(X\\)\uc5d0\uc11c \uc2e4\uc218\ub85c \uac00\ub294 \ubaa8\ub4e0 \ud568\uc218\uc758 \uc9d1\ud569 \\(\\mathbb R^X\\)\ub97c \uc0dd\uac01\ud558\uc790. \uae30\uc900 \ud568\uc218 \\(f\\in\\mathbb R^X\\), \uc720\ud55c\uc9d1\ud569 \\(F\\subseteq X\\), \\(\\varepsilon>0\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\nU(f;F,\\varepsilon)<br \/>\n=\\{g\\in\\mathbb R^X:|g(x)-f(x)|<\\varepsilon\\text{ for every }x\\in F\\}\n\\]\n\ud615\ud0dc\uc758 \uc9d1\ud569\ub4e4\uc744 \\(f\\)\uc758 \uae30\ubcf8 \uadfc\ubc29\uc73c\ub85c \uc0bc\ub294\ub2e4.<\/p>\n<p>[\uac01 \uc88c\ud45c\uc758 \uc2e4\uc218\uacf5\uac04 \\(\\mathbb R\\)\uc5d0 \ubcf4\ud1b5 \uc704\uc0c1\uc744 \uc8fc\uace0, \uc720\ud55c \uac1c\uc758 \uc88c\ud45c\uc5d0\ub9cc \uc5f4\ub9b0 \uc870\uac74\uc744 \uac70\ub294 \uc9d1\ud569\ub4e4\uc744 \uae30\uc800\ub85c \uc0bc\uc544 \\(\\mathbb R^X=\\prod_{x\\in X}\\mathbb R\\)\uc5d0 \uc8fc\ub294 \uc704\uc0c1\uc744 <span class=\"defined\">\uacf1\uc704\uc0c1<\/span>(product topology)\uc774\ub77c\uace0 \ud55c\ub2e4. \uac01 \uc88c\ud45c \ud3c9\uac00\ud568\uc218 \\(\\pi_x(f)=f(x)\\)\uac00 \ubaa8\ub450 \uc5f0\uc18d\uc774 \ub418\uac8c \ud558\ub294 \uac00\uc7a5 \uc57d\ud55c \uc704\uc0c1\uc774\uae30\ub3c4 \ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><a class=\"math-abs-series-ref\" title=\"Engelking, R. (1989). General Topology (revised and completed ed.). Sigma Series in Pure Mathematics, 6. Heldermann Verlag. \ucd9c\ud310\uc0ac \uc11c\uc9c0.\" href=\"#ref-Engelking1989\">[Engelking1989]<\/a>]<\/p>\n<p>\uc774 \uacf1\uc704\uc0c1\uc5d0\uc11c \ud568\uc218\uc5f4 \\((f_n)\\)\uc774 \\(f\\)\ub85c \uc218\ub834\ud560 \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \ubaa8\ub4e0 \\(x\\in X\\)\uc5d0 \ub300\ud558\uc5ec \uc2e4\uc218\uc5f4 \\((f_n(x))\\)\uc774 \\(f(x)\\)\ub85c \uc218\ub834\ud558\ub294 \uac83\uc774\ub2e4. \uc989 \uacf1\uc704\uc0c1\uc758 \uc218\uc5f4 \uc218\ub834\uc740 <span class=\"defined\">\uc810\ubcc4\uc218\ub834<\/span>(pointwise convergence)\uacfc \uc77c\uce58\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a><\/p>\n<p>\uc5ec\uae30\uc11c \uc815\uc758\uc5ed\uc758 \ud06c\uae30\uac00 \uc911\uc694\ud558\ub2e4. \\(X\\)\uac00 \uc720\ud55c\uc774\uba74 \uc720\ud55c \uac1c \uc88c\ud45c\uc758 \ubcf4\ud1b5 \uacf1\uac70\ub9ac\ub85c \ucda9\ubd84\ud558\ub2e4. \\(X\\)\uac00 \uac00\uc0b0 \ubb34\ud55c\uc774\uace0 \\(X=\\{x_1,x_2,\\ldots\\}\\)\ub85c \uc5f4\uac70\ud560 \uc218 \uc788\ub2e4\uba74<br \/>\n\\[<br \/>\nd(f,g)=\\sum_{n=1}^{\\infty}2^{-n}\\min\\{1,|f(x_n)-g(x_n)|\\}<br \/>\n\\]<br \/>\n\uac00 \uacf1\uc704\uc0c1\uc744 \uc720\ub3c4\ud55c\ub2e4. \ub530\ub77c\uc11c \uac00\uc0b0 \uc815\uc758\uc5ed\uc5d0\uc11c \uc810\ubcc4\uc218\ub834\uc758 \uc704\uc0c1\uc740 \uac70\ub9ac\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub2e4. \ubb38\uc81c\uac00 \uc0dd\uae30\ub294 \uac83\uc740 \\(X\\)\uac00 \ube44\uac00\uc0b0\uc77c \ub54c\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Engelking, R. (1989). General Topology (revised and completed ed.). Sigma Series in Pure Mathematics, 6. Heldermann Verlag. \ucd9c\ud310\uc0ac \uc11c\uc9c0.\" href=\"#ref-Engelking1989\">[Engelking1989]<\/a><\/p>\n<p>\ubaa8\ub4e0 \uac70\ub9ac\uacf5\uac04\uc740 <span class=\"defined\">\uc81c1\uac00\uc0b0<\/span>(first countable)\uc774\ub2e4. \uc989 \uac01 \uc810\ub9c8\ub2e4 \uadf8 \uc810\uc758 \ubaa8\ub4e0 \uadfc\ubc29\uc744 \uc138\ubd84\ud558\ub294 \uac00\uc0b0 \uac1c\uc758 \uad6d\uc18c\uae30\uc800\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/p>\n<p>[\uac70\ub9ac\uacf5\uac04\uc758 \uc810 \\(x\\)\uc5d0\uc11c \\(\\{B(x,1\/n):n\\in\\mathbb N\\}\\)\uc740 \uac00\uc0b0 \uad6d\uc18c\uae30\uc800\uc774\ub2e4. \\(V\\)\uac00 \\(x\\)\uc758 \uc5f4\ub9b0 \uadfc\ubc29\uc774\uba74 \uc5b4\ub5a4 \\(r>0\\)\uc5d0 \ub300\ud558\uc5ec \\(B(x,r)\\subseteq V\\)\uc774\uace0, \uc544\ub974\ud0a4\uba54\ub370\uc2a4 \uc131\uc9c8\uc5d0 \ub530\ub77c \\(1\/n < r\\)\uc778 \\(n\\)\uc744 \ud0dd\ud558\uba74 \\(B(x,1\/n)\\subseteq V\\)\uc774\uae30 \ub54c\ubb38\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall. Google Books.\" href=\"#ref-Munkres2000\">[Munkres2000]<\/a>]<\/p>\n<p>\uc774\uc81c \\(X\\)\uac00 \ube44\uac00\uc0b0\uc774\uace0 \\(\\mathbb R^X\\)\uc5d0 \uacf1\uc704\uc0c1\uc744 \uc8fc\uc5c8\ub2e4\uace0 \ud558\uc790. \uc5b4\ub5a4 \\(f\\in\\mathbb R^X\\)\uac00 \uac00\uc0b0 \uad6d\uc18c\uae30\uc800 \\(N_1,N_2,\\ldots\\)\ub97c \uac00\uc9c4\ub2e4\uace0 \uac00\uc815\ud574 \ubaa8\uc21c\uc744 \uc774\ub04c\uc5b4 \ub0b4\uc790. \uac01 \\(n\\)\uc5d0 \ub300\ud574 \\(f\\in U_n\\subseteq N_n\\)\uc778 \uae30\ubcf8 \uadfc\ubc29 \\(U_n\\)\uc744 \ud0dd\ud558\uace0, \\(U_n\\)\uc774 \uc870\uac74\uc744 \uac70\ub294 \uc720\ud55c\ud55c \uc88c\ud45c\ub4e4\uc758 \uc9d1\ud569\uc744 \\(F_n\\)\uc774\ub77c \ud558\uc790. \ud569\uc9d1\ud569 \\(\\bigcup_nF_n\\)\uc740 \uac00\uc0b0\uc774\ubbc0\ub85c, \ube44\uac00\uc0b0\uc9d1\ud569 \\(X\\)\uc5d0\ub294<br \/>\n\\[<br \/>\nx_0\\notin\\bigcup_{n=1}^{\\infty}F_n<br \/>\n\\]<br \/>\n\uc778 \uc810\uc774 \uc874\uc7ac\ud55c\ub2e4. \uc774\uc81c<br \/>\n\\[<br \/>\nV=\\{g\\in\\mathbb R^X:|g(x_0)-f(x_0)|<1\\}\n\\]\n\uc744 \uc7a1\uc73c\uba74 \\(V\\)\ub294 \\(f\\)\uc758 \uc5f4\ub9b0 \uadfc\ubc29\uc774\ub2e4. \uad6d\uc18c\uae30\uc800\uc758 \uc815\uc758\uc5d0 \ub530\ub974\uba74 \uc5b4\ub5a4 \\(N_n\\subseteq V\\)\uac00 \uc788\uc5b4\uc57c \ud558\uace0, \uadf8\ub7ec\uba74 \\(U_n\\subseteq V\\)\uc5ec\uc57c \ud55c\ub2e4. \uadf8\ub7ec\ub098 \\(U_n\\)\uc740 \uc88c\ud45c \\(x_0\\)\uc5d0 \uc544\ubb34 \uc870\uac74\ub3c4 \uac78\uc9c0 \uc54a\uc73c\ubbc0\ub85c, \\(x_0\\)\uc5d0\uc11c \\(f(x_0)\\)\uc640 1 \uc774\uc0c1 \ucc28\uc774 \ub098\ub294 \ud568\uc218\ub97c \ud3ec\ud568\ud55c\ub2e4. \ub530\ub77c\uc11c \\(U_n\\not\\subseteq V\\)\uc774\uace0 \ubaa8\uc21c\uc774\ub2e4.<\/p>\n<p>\uadf8\ub7ec\ubbc0\ub85c \\(X\\)\uac00 \ube44\uac00\uc0b0\uc774\uba74 \\(\\mathbb R^X\\)\uc758 \uacf1\uc704\uc0c1\uc740 \uc5b4\ub290 \uc810\uc5d0\uc11c\ub3c4 \uc81c1\uac00\uc0b0\uc774 \uc544\ub2c8\uba70, \ub530\ub77c\uc11c \uc5b4\ub5a4 \uac70\ub9ac\ub3c4 \uc774 \uc704\uc0c1\uc744 \uc720\ub3c4\ud560 \uc218 \uc5c6\ub2e4.<a class=\"math-abs-series-ref\" title=\"Engelking, R. (1989). General Topology (revised and completed ed.). Sigma Series in Pure Mathematics, 6. Heldermann Verlag. \ucd9c\ud310\uc0ac \uc11c\uc9c0.\" href=\"#ref-Engelking1989\">[Engelking1989]<\/a> <!-- \uc815\ud655\ud55c \uacb0\ub860\uc740 \u2018\uc810\ubcc4\uc218\ub834\uc774\ub77c\ub294 \ub9d0 \uc790\uccb4\uac00 \uc5b8\uc81c\ub098 \uac70\ub9ac\ub85c \ud45c\ud604\ub420 \uc218 \uc5c6\ub2e4\u2019\uac00 \uc544\ub2c8\ub77c, <strong>\ube44\uac00\uc0b0 \uc815\uc758\uc5ed\uc5d0\uc11c \uc810\ubcc4\uc218\ub834\uc744 \uc790\uc5f0\uc2a4\ub7fd\uac8c \uad6c\ud604\ud558\ub294 \uacf1\uc704\uc0c1\uc740 \uac70\ub9ac\ud654\ud560 \uc218 \uc5c6\ub2e4<\/strong>\ub294 \uac83\uc774\ub2e4.  \uc218\uc5f4\uc758 \uc218\ub834\ub9cc\uc73c\ub85c\ub294 \uc77c\ubc18 \uc704\uc0c1\uc758 \ubaa8\ub4e0 \uc815\ubcf4\ub97c \uacb0\uc815\ud560 \uc218 \uc5c6\ub2e4\ub294 \uc0ac\uc2e4\ub3c4 \uc5ec\uae30\uc11c \uc911\uc694\ud558\ub2e4. --><\/p>\n<h4>\uac70\ub9ac\ub97c \ubc84\ub9ac\uace0 \uc5f4\ub9b0\uc9d1\ud569\uc774 \ub0a8\ub2e4<\/h4>\n<p>\uc9c0\uae08\uae4c\uc9c0\uc758 \ucd94\uc0c1\ud654 \uacfc\uc815\uc744 \uc815\ub9ac\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<ul>\n<li>19\uc138\uae30 \ud574\uc11d\ud559\uc758 \uc5c4\ubc00\ud654 \uacfc\uc815\uc5d0\uc11c \uc5f0\uc18d\uc131\uc740 \u03b5-\u03b4\ub97c \uc0ac\uc6a9\ud55c \uc2dd\uc73c\ub85c \uc815\ub9ac\ub418\uc5c8\ub2e4. \ud2b9\ud788 \ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4\ub294 \uc774\ub7ec\ud55c \uc5c4\ubc00\ud55c \uc815\uc758\ub97c \uccb4\uacc4\ud654\ud558\uace0 \ud655\uc0b0\ud558\ub294 \ub370\uc5d0 \uacb0\uc815\uc801\uc778 \uc5ed\ud560\uc744 \ud588\ub2e4.<!-- \uc774\ub97c \ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4 \ud55c \uc0ac\ub78c\uc758 \ub2e8\ub3c5 \ubc1c\uba85\uc73c\ub85c \ud658\uc6d0\ud560 \uc218\ub294 \uc5c6\uc9c0\ub9cc, \uadf8\uc758 \uac15\uc758 \uc804\ud1b5\uc740 \uadf8 \uc815\uc2dd\ud654\uc758 \uccb4\uacc4\ud654\uc640 \ud655\uc0b0\uc5d0 \ud070 \uc5ed\ud560\uc744 \ud588\ub2e4. --><\/li>\n<li>\ud504\ub808\uc170\uc758 \ucd94\uc0c1 \uacf5\uac04 \uc5f0\uad6c\ub294 \uc6d0\uc18c\uc758 \uc815\uccb4 \ub300\uc2e0 \uac70\ub9ac\uc640 \uc218\ub834\uc758 \uad6c\uc870\ub97c \uc5f0\uad6c\ud558\uac8c \ud588\uace0, \ud604\ub300 \uac70\ub9ac\uacf5\uac04\uc5d0\uc11c\ub294 \uc2e4\uc218\u00b7\ud568\uc218\u00b7\uc218\uc5f4\uc744 \uac19\uc740 \uc5b8\uc5b4\ub85c \ub2e4\ub8f0 \uc218 \uc788\ub2e4.<\/li>\n<li>\ud558\uc6b0\uc2a4\ub3c4\ub974\ud504\uc758 \uadfc\ubc29 \uacf5\ub9ac\uc640 \uc774\ud6c4\uc758 \uc5ec\ub7ec \uacf5\ub9ac\ud654\ub294 \uac70\ub9ac \uc5c6\uc774 \uc5f4\ub9b0\uc9d1\ud569\ub9cc\uc73c\ub85c \uacf5\uac04\uacfc \uc5f0\uc18d\uc131\uc744 \ub2e4\ub8e8\ub294 \ud604\ub300 \uc704\uc0c1\uacf5\uac04\uc758 \ud2c0\ub85c \uc774\uc5b4\uc84c\ub2e4.<\/li>\n<li>\uac70\ub9ac\uacf5\uac04\uc5d0\uc11c\ub294 \u03b5-\u03b4 \uc5f0\uc18d\uc131\uacfc \uc704\uc0c1\uc801 \uc5f0\uc18d\uc131\uc774 \ub3d9\uce58\uc774\uc9c0\ub9cc, \ube44\uac00\uc0b0 \uacf1\uacf5\uac04\ucc98\ub7fc \uc790\uc5f0\uc2a4\ub7ec\uc6b4 \uc704\uc0c1\uc774 \uc5b4\ub5a4 \uac70\ub9ac\uc5d0\uc11c\ub3c4 \ub098\uc624\uc9c0 \uc54a\ub294 \uacf5\uac04\ub3c4 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n<\/ul>\n<p>\ucef4\ud329\ud2b8\uc131 \uc5ed\uc2dc \uac19\uc740 \uc77c\ubc18\ud654\uc758 \ud798\uc744 \ubcf4\uc5ec \uc900\ub2e4. \\(\\mathbb R^n\\)\uc5d0\uc11c\ub294 \ub2eb\ud798\uacfc \uc720\uacc4\uc131\uc774 \ucef4\ud329\ud2b8\uc131\uc744 \uc815\ud655\ud788 \ud2b9\uc9d5\uc9d3\uc9c0\ub9cc, \uc77c\ubc18 \uac70\ub9ac\uacf5\uac04\uacfc \ubb34\ud55c\ucc28\uc6d0 \ub178\ub984\uacf5\uac04\uc5d0\uc11c\ub294 \uadf8\ub807\uc9c0 \uc54a\ub2e4. \uc5f4\ub9b0\ub36e\uac1c\uc5d0 \uc758\ud55c \uc815\uc758\ub294 \uac70\ub9ac \uc5c6\uc774\ub3c4 \uc758\ubbf8\uac00 \uc788\uace0 \uc784\uc758\uc758 \uacf1\uc5d0\uc11c\ub3c4 \ubcf4\uc874\ub41c\ub2e4. \uc810\uc5f4 \ucef4\ud329\ud2b8\uc131\uc740 \uac70\ub9ac\uacf5\uac04\uc5d0\uc11c\ub294 \uc774\uc5d0 \ub3d9\uce58\uc774\uc9c0\ub9cc \uc77c\ubc18 \uc704\uc0c1\uacf5\uac04\uc5d0\uc11c\ub294 \uac08\ub77c\uc9c4\ub2e4. <!-- \ub530\ub77c\uc11c \u2018\uc720\uacc4\uc640 \ub2eb\ud798\uc774 \ud3d0\uae30\ub418\uc5c8\ub2e4\u2019\uae30\ubcf4\ub2e4\ub294, \uadf8\uac83\ub4e4\uc774 \ud2b9\uc815\ud55c \uacf5\uac04\uc5d0\uc11c\ub294 \uc5ec\uc804\ud788 \uc720\uc6a9\ud558\ub418 \uc77c\ubc18\uc801\uc778 \uc704\uc0c1\uc801 \uc815\uc758\ub97c \ub300\uc2e0\ud560 \uc218 \uc5c6\uac8c \ub418\uc5c8\ub2e4\uace0 \ub9d0\ud574\uc57c \ud55c\ub2e4. --><\/p>\n<p>\uc774 \uc5f0\uc7ac\uc5d0\uc11c\ub294 \ud2b9\uc815 \uacf5\uac04\uc758 \uc815\ub9ac\uc5d0\uc11c \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud558\ub358 \uc131\uc9c8\uc744 \ubd84\ub9ac\ud558\uc5ec \ub354 \ub113\uc740 \ub300\uc0c1\ub4e4\uc758 \uc815\uc758\ub85c \uc0bc\ub294 \ucd94\uc0c1\ud654 \ubc29\uc2dd\uc744 <span class=\"defined\">\uc815\ub9ac\uc758 \uc815\uc758 \uc2b9\uaca9<\/span>\uc774\ub77c\uace0 \ubd80\ub974\uae30\ub85c \ud55c\ub2e4. \ucef4\ud329\ud2b8\uc131\uacfc \uc5f0\uacb0\uc131\uc740 \uc774 \uad00\uc810\uc744 \uc798 \ubcf4\uc5ec \uc8fc\ub294 \ub300\ud45c\uc801\uc778 \uc0ac\ub840\uc774\ub2e4.<\/p>\n<p>\uc774\uc81c \uac70\ub9ac\ub97c \ub118\uc5b4\uc120 \ub2e4\uc74c \uc9c8\ubb38\uc740 \u2018\uae38\uc774\u2019\uc774\ub2e4. \ub2eb\ud78c\uad6c\uac04 \\([a,b]\\)\uc758 \uae38\uc774 \\(b-a\\)\ub97c \ub354 \ubcf5\uc7a1\ud55c \uc9d1\ud569\uc5d0\uae4c\uc9c0 \uc77c\uad00\ub418\uac8c \ud655\uc7a5\ud560 \uc218 \uc788\uc744\uae4c? <a href=\"..\/math-abstraction-08-measure-spaces\/\">8\ubd80<\/a>\uc5d0\uc11c\ub294 \uc774 \uc9c8\ubb38\uc744 \ub530\ub77c \ub974\ubca0\uadf8(Lebesgue)\uc758 \uce21\ub3c4\ub860\uacfc \ud655\ub960\ub860\uc73c\ub85c \ub098\uc544\uac04\ub2e4.<\/p>\n<h4>\ucc38\uace0\ubb38\ud5cc<\/h4>\n<ul>\n<li id=\"ref-Grabiner1983\">[Grabiner1983] Grabiner, J. V. (1983). \u201cWho Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus.\u201d <i>The American Mathematical Monthly<\/i>, 90(3), 185\u2013194. <a href=\"https:\/\/doi.org\/10.1080\/00029890.1983.11971185\">https:\/\/doi.org\/10.1080\/00029890.1983.11971185<\/a>, <a href=\"https:\/\/scholarship.claremont.edu\/pitzer_fac_pub\/122\/\">Claremont Colleges Scholarship<\/a>.<\/li>\n<li id=\"ref-Frechet1906\">[Frechet1906] Fr\u00e9chet, M. (1906). \u201cSur quelques points du calcul fonctionnel.\u201d <i>Rendiconti del Circolo Matematico di Palermo<\/i>, 22, 1\u201372. <a href=\"https:\/\/doi.org\/10.1007\/BF03018603\">https:\/\/doi.org\/10.1007\/BF03018603<\/a>.<\/li>\n<li id=\"ref-Taylor1982\">[Taylor1982] Taylor, A. E. (1982). \u201cA Study of Maurice Fr\u00e9chet: I. His Early Work on Point Set Theory and the Theory of Functionals.\u201d <i>Archive for History of Exact Sciences<\/i>, 27, 233\u2013295. <a href=\"https:\/\/doi.org\/10.1007\/BF00327860\">https:\/\/doi.org\/10.1007\/BF00327860<\/a>.<\/li>\n<li id=\"ref-Hausdorff1914\">[Hausdorff1914] Hausdorff, F. (1914). <i>Grundz\u00fcge der Mengenlehre<\/i>. Leipzig: Veit &amp; Comp., <a href=\"https:\/\/archive.org\/details\/grundzgedermen00hausuoft\">Internet Archive<\/a>.<\/li>\n<li id=\"ref-Kuratowski1922\">[Kuratowski1922] Kuratowski, C. (1922). \u201cSur l\u2019op\u00e9ration \u0100 de l\u2019Analysis Situs.\u201d <i>Fundamenta Mathematicae<\/i>, 3, 182\u2013199. <a href=\"https:\/\/doi.org\/10.4064\/fm-3-1-182-199\">https:\/\/doi.org\/10.4064\/fm-3-1-182-199<\/a>. \uc6d0\ubb38: <a href=\"https:\/\/eudml.org\/doc\/213290\">EuDML<\/a>.<\/li>\n<li id=\"ref-Munkres2000\">[Munkres2000] Munkres, J. R. (2000). <i>Topology<\/i> (2nd ed.). Prentice Hall. <a href=\"https:\/\/books.google.com\/books?id=XjoZAQAAIAAJ\">Google Books<\/a>.<\/li>\n<li id=\"ref-AndreEtAl2013\">[AndreEtAl2013] Andre, N. R., Engdahl, S. M., &amp; Parker, A. E. (2013). \u201cAn Analysis of the First Proofs of the Heine\u2013Borel Theorem.\u201d <i>Convergence<\/i>. <a href=\"https:\/\/doi.org\/10.4169\/loci003890\">https:\/\/doi.org\/10.4169\/loci003890<\/a>.<\/li>\n<li id=\"ref-RamanSundstrom2015\">[RamanSundstrom2015] Raman-Sundstr\u00f6m, M. (2015). \u201cA Pedagogical History of Compactness.\u201d <i>The American Mathematical Monthly<\/i>, 122(7), 619\u2013635. <a href=\"https:\/\/doi.org\/10.4169\/amer.math.monthly.122.7.619\">https:\/\/doi.org\/10.4169\/amer.math.monthly.122.7.619<\/a>, <a href=\"https:\/\/arxiv.org\/abs\/1006.4131\">arXiv:1006.4131<\/a>.<\/li>\n<li id=\"ref-HunterNachtergaele2001\">[HunterNachtergaele2001] Hunter, J. K., &amp; Nachtergaele, B. (2001). <i>Applied Analysis<\/i>. World Scientific. <a href=\"https:\/\/doi.org\/10.1142\/4319\">https:\/\/doi.org\/10.1142\/4319<\/a>, <a href=\"https:\/\/www.math.ucdavis.edu\/~bxn\/applied_analysis.pdf\">PDF<\/a>.<\/li>\n<li id=\"ref-Tychonoff1935\">[Tychonoff1935] Tychonoff, A. (1935). \u201c\u00dcber einen Funktionenraum.\u201d <i>Mathematische Annalen<\/i>, 111, 762\u2013766. <a href=\"https:\/\/doi.org\/10.1007\/BF01472255\">https:\/\/doi.org\/10.1007\/BF01472255<\/a>, <a href=\"https:\/\/eudml.org\/doc\/159809\">EuDML<\/a>.<\/li>\n<li id=\"ref-Kelley1950\">[Kelley1950] Kelley, J. L. (1950). \u201cThe Tychonoff Product Theorem Implies the Axiom of Choice.\u201d <i>Fundamenta Mathematicae<\/i>, 37(1), 75\u201376. <a href=\"https:\/\/eudml.org\/doc\/213229\">EuDML<\/a>.<\/li>\n<li id=\"ref-Engelking1989\">[Engelking1989] Engelking, R. (1989). <i>General Topology<\/i> (revised and completed ed.). Sigma Series in Pure Mathematics, 6. Heldermann Verlag. <a href=\"https:\/\/www.heldermann.de\/SSPM\/SSPM06\/sspm06.htm\">https:\/\/www.heldermann.de\/SSPM\/SSPM06\/sspm06.htm<\/a>.<\/li>\n<\/ul>\n<h4>\uc800\uc791\uad8c<\/h4>\n<p>\uc774\uc2ac\ube44, 2026. designeralice\uff20daum.net.<\/p>\n<div class=\"math-abs-series-contents\">\n<p class=\"math-abs-series-menu-title\"><a href=\"..\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654<\/a><\/p>\n<ol class=\"math-abs-series-menu-list\">\n        <!-- \ud604\uc7ac \ud398\uc774\uc9c0\uc5d0 \ud574\ub2f9\ud558\ub294 li \ud0dc\uadf8\uc5d0 class=\"math-abs-series-current-page\" \uc18d\uc131 \ucd94\uac00 --><\/p>\n<li><a href=\"..\/math-abstraction-01-essence\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uae30\ubcf8 \uac1c\ub150<\/a><\/li>\n<li><a href=\"..\/math-abstraction-02-implicit-era\/\">\ucd08\uae30 \uc218\ud559\uc5d0\uc11c\uc758 \uc554\ubb35\uc801 \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-03-algebraic-symbols\/\">\ub300\uc218\uc801 \uae30\ud638\uc640 \uc5f0\uc0b0 \ubc95\uce59<\/a><\/li>\n<li><a href=\"..\/math-abstraction-04-axiomatic-method\/\">\uacf5\ub9ac\uc801 \ubc29\ubc95\uc5d0 \uc758\ud55c \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-05-mathematical-structures\/\">\uc218\ud559\uc801 \uad6c\uc870\uc640 \ubc94\uc8fc\ub860<\/a><\/li>\n<li><a href=\"..\/math-abstraction-06-vector-spaces\/\">\ubca1\ud130\uacf5\uac04\uacfc \uc120\ud615 \uad6c\uc870<\/a><\/li>\n<li class=\"math-abs-series-current-page\"><a href=\"..\/math-abstraction-07-topological-spaces\/\">\uac70\ub9ac\uacf5\uac04\uacfc \uc704\uc0c1\uacf5\uac04<\/a><\/li>\n<li><a href=\"..\/math-abstraction-08-measure-spaces\/\">\uce21\ub3c4\uacf5\uac04\uacfc \ud655\ub960\uacf5\uac04<\/a><\/li>\n<li><a href=\"..\/math-abstraction-09-cognitive-process\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uc778\uc9c0\uc640 \ud559\uc2b5<\/a><\/li>\n<li><a href=\"..\/math-abstraction-10-optimal-generality\/\">\ud604\ub300 \uc218\ud559 \uc5f0\uad6c\uc5d0\uc11c\uc758 \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-11-topography\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \ubc29\ubc95\uacfc \ucca0\ud559<\/a><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p><!-- class=\"math-abs-series\" --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>6\ubd80\uc758 \ub9d0\ubbf8\uc5d0\uc11c \uc644\ube44\uc131\uc744 \uc815\uc758\ud560 \ub54c, \uc6b0\ub9ac\ub294 \u2018\ucf54\uc2dc\uc218\uc5f4\uc774 \uc5b4\ub5a4 \uc810\uc73c\ub85c \uc218\ub834\ud55c\ub2e4\u2019\ub294 \uc870\uac74\uc744 \uc0ac\uc6a9\ud588\ub2e4. \uadf8\ub7f0\ub370 \u2018\uc218\ub834\ud55c\ub2e4\u2019, \uace7 \ud55c \uc810\uc5d0 \u2018\uac00\uae4c\uc6cc\uc9c4\ub2e4\u2019\ub294 \ub9d0\uc774 \uc815\ud655\ud788 \ubb34\uc5c7\uc744 \ub73b\ud558\ub294\uc9c0\ub294 \uae4a\uc774 \ub2e4\ub8e8\uc9c0 \uc54a\uc558\ub2e4. \uc2e4\ud574\uc11d\uc5d0\uc11c \uac00\uae4c\uc6c0\uc744 \ub098\ud0c0\ub0b4\ub294 \uac00\uc7a5 \uc775\uc219\ud55c \ubaa8\ud615\uc740 \uc2e4\uc9c1\uc120 \uc704\uc758 \uac70\ub9ac \\(|x-y|\\)\uc774\ub2e4. \uadf8\ub7ec\ub098 \ud568\uc218\ub098 \uc218\uc5f4\ucc98\ub7fc \ub354 \uc77c\ubc18\uc801\uc778 \ub300\uc0c1\uc744 \ub2e4\ub8e8\ub824\uba74 \ubb34\uc5c7\uc744 \uac70\ub9ac\ub85c \uc0bc\uc744\uc9c0\ubd80\ud130 \uc0c8\ub85c \uc815\ud574\uc57c \ud558\uba70, \uc5b4\ub5a4 \uacf5\uac04\uc758 \uc790\uc5f0\uc2a4\ub7ec\uc6b4 \uac00\uae4c\uc6c0\uc740 \uc544\uc608 \ud558\ub098\uc758 \uac70\ub9ac\ub85c \ud45c\ud604\ub418\uc9c0 \uc54a\uae30\ub3c4 \ud55c\ub2e4. \uc774 \uae00\uc5d0\uc11c\ub294 \uc2e4\uc218\uc758 \uac70\ub9ac\uc5d0\uc11c \uac70\ub9ac\uacf5\uac04\uc73c\ub85c, \ub2e4\uc2dc&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9726,"menu_order":700,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-9747","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9747","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=9747"}],"version-history":[{"count":18,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9747\/revisions"}],"predecessor-version":[{"id":10054,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9747\/revisions\/10054"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9726"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=9747"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}