{"id":21475,"date":"2015-06-02T00:50:10","date_gmt":"2015-06-01T16:50:10","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=21475"},"modified":"2018-08-01T15:52:21","modified_gmt":"2018-08-01T07:52:21","slug":"%e3%80%90%e6%95%b8%e5%ad%b8%e6%a6%82%e5%bf%b5%e3%80%91%e9%80%99%e7%89%87%e5%9c%9f%e5%9c%b0%e7%9a%84%e6%a8%a3%e8%b2%8c%ef%bc%8d%ef%bc%8d%e6%b7%ba%e8%ab%87%e6%8b%93%e6%92%b2%e5%ad%b8","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=21475","title":{"rendered":"\u3010\u6578\u5b78\u6982\u5ff5\u3011\u9019\u7247\u571f\u5730\u7684\u6a23\u8c8c\uff0d\uff0d\u6dfa\u8ac7\u62d3\u64b2\u5b78"},"content":{"rendered":"<figure id=\"attachment_21478\" aria-describedby=\"caption-attachment-21478\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-21478\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/05\/M\u00f6bius_strip.jpg\" alt=\"\u5716\u7247\u4f86\u6e90\uff5c\u7dad\u57fa\u767e\u79d1\" width=\"650\" height=\"403\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/05\/M\u00f6bius_strip.jpg 1328w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/05\/M\u00f6bius_strip-300x186.jpg 300w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/05\/M\u00f6bius_strip-1024x635.jpg 1024w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/05\/M\u00f6bius_strip-800x496.jpg 800w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><figcaption id=\"caption-attachment-21478\" class=\"wp-caption-text\">\u5716\u7247\u4f86\u6e90\uff5c\u7dad\u57fa\u767e\u79d1<\/figcaption><\/figure>\n<p><strong>\u64b0\u6587\uff5c<\/strong>\u5433\u5982\u5cf0<\/p>\n<p>\u5728<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=21248\" target=\"_blank\" rel=\"noopener noreferrer\">\u4e0a\u4e00\u7bc7\u6587\u7ae0<\/a>\u4e2d\uff0c\u6211\u5011\u5728\u6700\u5f8c\u7559\u4e0b\u4e86\u4e00\u500b\u554f\u984c\uff1a\u9019\u500b\u4e16\u754c\u662f\u5426\u5b58\u5728\u771f\u7684\u9023\u7e8c\u7684\u6771\u897f\u5462\uff1f\u4eca\u5929\u5c31\u8b93\u6211\u5011\u4f86\u56de\u7b54\u9019\u500b\u554f\u984c\u5427\uff01\u4f46\u5728\u56de\u7b54\u9019\u500b\u554f\u984c\u4e4b\u524d\uff0c\u6211\u5011\u8981\u5148\u8ac7\u4e00\u8ac7\u6211\u5011\u9019\u584a\u571f\u5730\u7684\u6a23\u8c8c\u3002<\/p>\n<p>\u554a\uff1f\u4ec0\u9ebc\uff1f\u9019\u8ddf\u571f\u5730\u7684\u6a23\u8c8c\u4e5f\u6709\u95dc\u4fc2\uff1f<\/p>\n<p>\u9019\u9ebc\u8aaa\u597d\u4e86\uff0c\u9019\u662f\u8a9e\u8a00\u4e0a\u7684\u95dc\u4fc2\u3002\u5728\u53e4\u5e0c\u81d8\uff0c\u300c\u571f\u5730\u6a23\u8c8c\u7684\u5b78\u554f\u300d\u5c31\u662f\u7531\u5169\u500b\u5b57\u6240\u62fc\u8d77\u4f86\u7684\uff1a\u201d\u03c4\u03cc\u03c0\u03bf\u03c2\u201d\u4ee3\u8868\u300c\u571f\u5730(place)\u300d\u7684\u610f\u601d\u3001\u201d\u03bb\u03cc\u03b3\u03bf\u03c2\u201d\u4ee3\u8868\u300c\u5b78\u554f(study)\u300d\u7684\u610f\u601d\uff0c\u56e0\u6b64\u201d \u03c4\u03bf\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b1\u201d\u5c31\u662f\u300c\u7814\u7a76\u571f\u5730\u7684\u5b78\u554f\u300d\u7684\u610f\u601d\uff0c\u9019\u500b\u5b57\u7ffb\u8b6f\u6210\u4e2d\u6587\u5c31\u6210\u4e86\u73fe\u5728\u5927\u5bb6\u8033\u4e2d\u7684\u300c\u62d3\u64b2(topology)\u300d\u3002\u5728\u5341\u4e5d\u4e16\u7d00\u4e2d\u671f\uff0c\u6578\u5b78\u5bb6\u5011\u628a\u9019\u500b\u6982\u5ff5\u5f15\u9032\u5230\u6578\u5b78\u88e1\u9762\uff0c\u7576\u6642\u4e3b\u8981\u7684\u554f\u984c\u5c31\u662f\u70ba\u4e86\u7814\u7a76\u6578\u5b78\u5206\u6790\uff0c\u8b1b\u5f97\u7c21\u55ae\u4e00\u9ede\uff0c\u5c31\u662f\u5728\u7814\u7a76\u4e00\u4e9b\u8ddf\u9023\u7e8c\u51fd\u6578\u6709\u95dc\u7684\u554f\u984c\u3002<!--more--><\/p>\n<p>\u90a3\u300c\u62d3\u64b2\u300d\u5230\u5e95\u662f\u4ec0\u9ebc\u5462\uff1f\u6578\u5b78\u5bb6\u7d66\u4e86\u4e0b\u9762\u9019\u500b\u5bb9\u6613\u4ee4\u4eba\u982d\u660f\u7684\u5b9a\u7fa9\uff1a<\/p>\n<p><strong><span style=\"color: #008080;\">\u5c0d\u65bc\u4efb\u610f\u4e00\u500b\u96c6\u5408X\uff08\u5168\u7a7a\u9593\uff09\uff0c\u5982\u679c\u5b58\u5728\u4e00\u500bX\u7684\u5b50\u96c6\u5408\u7684\u96c6\u5408T\u4f7f\u5f97T\u6eff\u8db3\u4e0b\u5217\u4e09\u500b\u689d\u4ef6\uff1a<\/span><\/strong><\/p>\n<ol>\n<li><strong><span style=\"color: #008080;\">X\u53ca\u7a7a\u96c6\u5408\u90fd\u843d\u5728T\u88e1\u9762<\/span><\/strong><\/li>\n<li><strong><span style=\"color: #008080;\">T\u88e1\u9762\u7684\u96c6\u5408\u7684\u4efb\u610f\u806f\u96c6\u4e5f\u843d\u5728T\u88e1\u9762<\/span><\/strong><\/li>\n<li><strong><span style=\"color: #008080;\">T\u88e1\u9762\u7684\u96c6\u5408\u7684\u6709\u9650\u4ea4\u96c6\u4e5f\u843d\u5728T\u88e1\u9762<\/span><\/strong><\/li>\n<\/ol>\n<p><strong><span style=\"color: #008080;\">\u90a3\u9ebc\uff0c\u6211\u5011\u4fbf\u7a31T\u70baX\u7684\u62d3\u64b2<\/span><\/strong><\/p>\n<p>\u8981\u5177\u9ad4\u5730\u8aaa\u660e\u9019\u500b\u5b9a\u7fa9\uff0c\u6211\u5011\u5fc5\u9808\u501f\u52a9\u4e00\u4e9b\u4f8b\u5b50\u4f86\u5e6b\u52a9\u6211\u5011\u4e86\u89e3\u3002\u9019\u500b\u4f8b\u5b50\u5fc5\u9808\u8981\u8acb\u8b80\u8005\u5011\u56de\u60f3\u7576\u521d\u5728\u5b78\u7fd2\u5fae\u7a4d\u5206\u6642\u6642\u5e38\u4f7f\u7528\u7684\u300c\u958b\u5340\u9593(open interval)\u300d\uff1a\u5728\u5be6\u6578\u7dda\u4e0a\u6211\u5011\u5b9a\u7fa9\u4e00\u500b\u958b\u5340\u9593(a,b)\u70ba\u4e00\u500b\u641c\u96c6\u6240\u6709\u5927\u65bca\u4e14\u5c0f\u65bcb\u7684\u6240\u6709\u5be6\u6578\u7684\u96c6\u5408\u3002<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-21476\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/05\/646131.png\" alt=\"646131\" width=\"363\" height=\"103\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/05\/646131.png 363w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/05\/646131-300x85.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>\u4e26\u4e14\uff0c\u6211\u5011\u4e5f\u628a\u6574\u500b\u5be6\u6578\u7dda\u53ca\u7a7a\u96c6\u5408\u5b9a\u70ba\u958b\u5340\u9593\u3002\u90a3\u9ebc\u7576\u6211\u5011\u8003\u616eT={\u6240\u6709\u958b\u5340\u9593}\uff0c\u6211\u5011\u53ef\u4ee5\u767c\u73fe\uff1a\u6574\u500b\u5be6\u6578\u7dda\u53ca\u7a7a\u96c6\u5408\u90fd\u5728T\u88e1\u9762\u3001\u958b\u5340\u9593\u5011\u5f97\u4efb\u610f\u806f\u96c6\u4e5f\u662f\u958b\u5340\u9593\u3001\u958b\u5340\u9593\u7684\u6709\u9650\u4ea4\u96c6\u4e5f\u662f\u958b\u5340\u9593\u3002\u65bc\u662fT\u5c31\u6eff\u8db3\u4e86\u6211\u5011\u4e0a\u9762\u7d66\u7684\u62d3\u64b2\u7684\u5b9a\u7fa9\uff0c\u4e5f\u5c31\u662f\u8aaa\uff0cT\u5c31\u662f\u5be6\u6578\u7dda\u7684\u62d3\u64b2\u3002<\/p>\n<p>\u5f9e\u9019\u500b\u4f8b\u5b50\u4f86\u8aaa\uff0c\u6211\u5011\u53ef\u4ee5\u767c\u73fe\uff1a\u539f\u4f86\u6211\u5011\u4e0a\u9762\u7d66\u5f97\u90a3\u500b\u62d3\u64b2\u7684\u5b9a\u7fa9\u53ea\u662f\u5728\u5b9a\u7fa9\u4e00\u500b\u96c6\u5408\u88e1\u9762\u7684\u958b\u5340\u9593\u662f\u4ec0\u9ebc\u800c\u5df2\u3002\u8b1b\u5230\u9019\u88e1\uff0c\u4f60\u6216\u8a31\u6703\u554f\u8aaa\uff1a\u90a3\u958b\u5340\u9593\u53c8\u4ee3\u8868\u8457\u4ec0\u9ebc\uff1f\u6211\u5011\u5e79\u561b\u5b9a\u7fa9\u4e00\u500b\u96c6\u5408\u5f97\u958b\u5340\u9593\uff1f<\/p>\n<p>\u5176\u5be6\u7c21\u55ae\u4f86\u8aaa\uff0c\u958b\u5340\u9593\u5c31\u662f\u544a\u8a34\u4f60\u54ea\u4e9b\u6771\u897f\u5f88\u9760\u8fd1\uff0c\u4e5f\u5c31\u662f\u8aaa\u54ea\u4e9b\u6771\u897f\u5f0f\u9130\u5c45\uff1a\u7576\u5169\u500b\u6578\u5f88\u9760\u8fd1\u6642\uff0c\u4ee3\u8868\u4ed6\u5011\u662f\u9130\u5c45\uff0c\u4e5f\u5c31\u662f\u8aaa\u6703\u5b58\u5728\u4e00\u500b\u5c0d\u5169\u500b\u6578\u90fd\u9130\u8fd1\u7684\u5340\u57df(neighborhood)\u628a\u5169\u500b\u6578\u90fd\u5305\u542b\u5728\u88e1\u9762\uff0c\u800c\u8d8a\u9760\u8fd1\u7684\u6578\u5c31\u53ef\u4ee5\u627e\u5230\u8d8a\u5c0f\u7684\u958b\u5340\u9593\u540c\u6642\u5305\u542b\u9019\u5169\u500b\u6578\u3002\u8b6c\u5982\u8aaa\u5927\u5b89\u5340\u8207\u4e2d\u6b63\u5340\u5f88\u9760\u8fd1\uff0c\u6240\u4ee5\u53ef\u4ee5\u7528\u53f0\u5317\u5e02\u505a\u70ba\u4e00\u500b\u9130\u8fd1\u7684\u5340\u57df\u4f86\u5c07\u5169\u500b\u76f4\u8f44\u5e02\u90fd\u5305\u542b\u5728\u88e1\u9762\uff0c\u5728\u9019\u500b\u62d3\u64b2\u88e1\u982d\uff0c\u4f60\u6240\u4f7f\u7528\u7684\u300c\u958b\u5340\u9593\u300d\u5c31\u662f\u300c\u5168\u81fa\u7063\u7684\u7e23\u5e02\u300d\u3001\u800c\u5168\u7a7a\u9593\u662f\u300c\u81fa\u7063\u300d\uff1b\u53c8\u6216\u8005\u8aaa\u4f60\u53ef\u4ee5\u628a\u5168\u4e16\u754c\u8996\u70ba\u4e00\u500b\u5168\u7a7a\u9593\u3001\u90a3\u9ebc\u81fa\u7063\u7684\u5404\u500b\u7e23\u5e02\u5c31\u6703\u5f7c\u6b64\u9760\u5f97\u5f88\u8fd1\uff0c\u8207\u5927\u9678\u7684\u5c31\u6703\u8ddd\u96e2\u9059\u9060\u3002<\/p>\n<p>\u56de\u5230\u6211\u5011\u7684\u5b9a\u7fa9\u4e0a\uff0c\u7531\u65bc\u6211\u5011\u7684\u5b9a\u7fa9\u662f\u53ef\u4ee5\u5b9a\u7fa9\u5728\u4efb\u4f55\u4e00\u500b\u96c6\u5408\u4e0a\u800c\u4e0d\u4e00\u5b9a\u8981\u5b9a\u5728\u5be6\u6578\u7dda\u4e0a\uff0c\u65bc\u662f\u6211\u5011\u628aT\u88e1\u9762\u7684\u9019\u4e9b\u96c6\u5408\u7a31\u70ba\u300c\u958b\u96c6(open set)\u300d\uff0c\u6216\u8005\u5c31\u76f4\u63a5\u7a31\u505aopen neighborhood\u3002<\/p>\n<p>\u800c\u6211\u5011\u525b\u525b\u5728\u4e0d\u540c\u7684\u5168\u7a7a\u9593\u4e0a\u770b\u5230\u4e86\u4e0d\u4e00\u6a23\u7684\u62d3\u64b2\uff0c\u90a3\u9ebc\u662f\u4e0d\u662f\u540c\u4e00\u500b\u7a7a\u9593\u4e0a\u53ef\u4ee5\u5b9a\u51fa\u4e0d\u4e00\u6a23\u7684\u62d3\u64b2\u5462\uff1f\u7b54\u6848\u662f\uff1a\u662f\u7684\u3002\u6700\u7c21\u55ae\u7684\u5169\u500b\u4f8b\u5b50\u5c31\u662f\uff1a\u5c0d\u65bc\u4efb\u4e00\u4e00\u500b\u96c6\u5408X\uff0c\u6211\u53ef\u4ee5\u53ea\u8490\u96c6X\u8207\u7a7a\u96c6\u5408\u5230T\u88e1\u9762\uff0c\u90a3\u9ebcT\u6703\u6eff\u8db3\u6211\u5011\u7684\u689d\u4ef6\uff08\u6578\u5b78\u5bb6\u5011\u7a31\u9019\u6a23\u7684\u62d3\u64b2\u70ba\u5bc6\u8457\u62d3\u64b2(tirvial topology)\uff09\uff1b\u53e6\u4e00\u500b\u5247\u662f\uff0c\u6211\u628aX\u88e1\u6240\u6709\u7684\u96c6\u5408\u90fd\u8490\u96c6\u5230T\u88e1\u9762\uff0c\u90a3\u9ebcT\u4e5f\u6703\u6eff\u8db3\u6211\u5011\u7d66\u7684\u62d3\u64b2\u7684\u689d\u4ef6\uff08\u6578\u5b78\u5bb6\u5011\u7a31\u9019\u6a23\u7684\u62d3\u64b2\u70ba\u96e2\u6563\u62d3\u64b2(discrete topology)\uff09\u3002<\/p>\n<p>\u8aaa\u5230\u9019\u88e1\uff0c\u6216\u8a31\u4f60\u6703\u4e0d\u7981\u7d0d\u60b6\uff1a\u9019\u5230\u5e95\u8207\u9023\u7e8c\u4e0d\u9023\u7e8c\u6709\u4ec0\u9ebc\u95dc\u4fc2\u5462\uff1f\u5728\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u5011\u5df2\u7d93\u6709\u63d0\u5230\uff1a<em>\u5982\u679c\u6709\u4e00\u500b\u5b58\u5728\u5169\u500b\u62d3\u6a38\u7a7a\u9593\u4e4b\u9593\u7684\u6620\u5c04\uff0c\u9019\u500b\u6620\u5c04\u5728\u67d0\u4e00\u9ede\u9023\u7e8c\u82e5\u4e14\u70ba\u82e5\u4efb\u610f\u5305\u542b\u9019\u500b\u9ede\u51fd\u6578\u503c\u7684\u958b\u96c6\u7684\u9006\u5411\u662f\u5305\u542b\u9019\u500b\u9ede\u7684\u67d0\u500b\u958b\u96c6<\/em>\u3002\u6240\u4ee5\uff0c\u8aaa\u7a7f\u4e86\uff0c\u4e00\u500b\u9023\u7e8c\u6620\u5c04\u53ea\u662f\u5728\u8aaa\u660e\u5169\u500b\u7a7a\u9593\u4e2d\u7684\u62d3\u64b2\u6709\u591a\u9ebc\u96f7\u540c\u3002<\/p>\n<p>\u65bc\u662f\uff0c\u7576\u6211\u5011\u8003\u616e\u6211\u5011\u73fe\u5be6\u7a7a\u9593\u4e2d\u7684\u62d3\u64b2\u70ba\u5bc6\u8457\u62d3\u64b2\u6642\uff0c\u90a3\u9ebc\u6240\u6709\u5728\u539f\u672c\u7684\u62d3\u64b2\u4e4b\u4e0b\u4e0d\u9023\u7e8c\u7684\u4e8b\u7269\uff0c\u7a81\u7136\u9593\u5c31\u8b8a\u5f97\u975e\u5e38\u7684\u9023\u7e8c\u4e86\uff01<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/line.me\/R\/ti\/p\/%40fcx6182w\" target=\"_blank\" rel=\"noopener noreferrer\"><img decoding=\"async\" class=\"alignnone\" src=\"https:\/\/scdn.line-apps.com\/n\/line_add_friends\/btn\/zh-Hant.png\" alt=\"\u52a0\u5165\u597d\u53cb\" width=\"212\" height=\"36\" border=\"0\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u64b0\u6587\uff5c\u5433\u5982\u5cf0 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