{"id":967,"date":"2021-07-25T16:55:23","date_gmt":"2021-07-25T08:55:23","guid":{"rendered":"https:\/\/www.caiqinyi.cn\/?p=967"},"modified":"2025-02-26T11:19:12","modified_gmt":"2025-02-26T03:19:12","slug":"gluing_map","status":"publish","type":"post","link":"https:\/\/www.caiqinyi.cn\/index.php\/2021\/07\/25\/gluing_map\/","title":{"rendered":"\u7c98\u5408\u6620\u5c04"},"content":{"rendered":"<p><script type=\"text\/javascript\" async src=\"https:\/\/www.caiqinyi.cn\/wp-content\/MathJax\/MathJax.js?config=TeX-AMS_CHTML\">\n<\/script><br \/>\n<script type=\"text\/x-mathjax-config\">\n    MathJax.Hub.Config({\n        tex2jax: {inlineMath: [['$','$']]},\n        TeX: {equationNumbers: {autoNumber: [\"AMS\"], useLabelIds: true}},\n        \"HTML-CSS\": {linebreaks: {automatic: true}},\n        SVG: {linebreaks: {automatic: true}}\n    });\n<\/script><\/p>\n<p>\u8fd9\u5468\u5468\u672b\u522e\u53f0\u98ce, \u6240\u4ee5\u53ea\u80fd&#8221;\u88ab\u8feb&#8221;\u5446\u5728\u5bb6\u91cc2333 \u8fd9\u5468\u4e3b\u8981\u9488\u5bf9\u7c98\u5408\u6620\u5c04\u7684\u90e8\u5206\u4f5c\u4e86\u4e00\u4e9b\u5b66\u4e60\u7684\u8865\u5145, \u4e4b\u524d\u5728\u770b\u4e66\u7684\u65f6\u5019\u5bf9\u4e66\u4e0a\u4e00\u4e9b\u7c98\u5408\u7684\u4f8b\u5b50\u5e76\u4e0d\u7406\u89e3, \u6240\u4ee5\u4fbf\u5728B\u7ad9\u4e0a\u627e\u4e86\u4e2a\u62d3\u6251\u7cfb\u5217\u7684\u89c6\u9891\u8fdb\u884c\u5b66\u4e60, \u786e\u5b9e\u6709\u4e86\u8fdb\u4e00\u6b65\u7684\u7406\u89e3, \u672c\u6587\u4fbf\u662f\u8bb0\u5f55\u4e00\u4e0b\u7c98\u5408\u6620\u5c04\u76f8\u5173\u7684\u5185\u5bb9. (PS: \u4e0d\u5f97\u4e0d\u8bf4, \u62d3\u6251\u7cfb\u5217\u7684\u4e2d\u6587\u89c6\u9891\u6559\u7a0b\u5b9e\u5728\u662f\u592a\u5c11\u4e86, \u5728\u6b64\u518d\u6b21\u611f\u8c22\u6d59\u7406\u5de5\u7684\u5e84\u6653\u6ce2\u8001\u5e08\u7684\u8f9b\u52e4\u521b\u4f5c~~~)<\/p>\n<p><!--more--><\/p>\n<p><strong>\u53c2\u8003\u6750\u6599<\/strong><br \/>\n1. <a href=\"https:\/\/www.bilibili.com\/video\/BV1P7411N7fW?p=20\">\u57fa\u7840\u62d3\u6251\u5b66<\/a><\/p>\n<p>\u7c98\u5408\u6620\u5c04\u76f8\u5173\u7684\u5185\u5bb9\u5176\u5b9e\u8fd8\u662f\u86ee\u591a\u7684, \u5177\u4f53\u7ec6\u8282\u53ef\u4ee5\u53c2\u8003\u5e84\u6653\u6ce2\u8001\u5e08\u7684\u89c6\u9891(P20-P23), \u6211\u89c9\u5f97\u7ec6\u8282\u8bb2\u89e3\u5f97\u5341\u5206\u5230\u4f4d~ \u63a5\u4e0b\u6765\u53ea\u8bb0\u5f55\u51e0\u4e2a\u9700\u8981\u6ce8\u610f\u7684\u70b9.<\/p>\n<p><strong>1. \u5546\u6620\u5c04\u53ef\u4ee5\u65e2\u4e0d\u662f\u5f00\u6620\u5c04\u4e5f\u4e0d\u662f\u95ed\u6620\u5c04<\/strong><\/p>\n<p>\u8003\u8651\u4e00\u4e0b\u5546\u6620\u5c04\u7684\u5b9a\u4e49: \u8bbe$X,Y$\u4e3a\u4e24\u4e2a\u62d3\u6251\u7a7a\u95f4, $f:X \\to Y$\u662f\u4e00\u4e2a\u5c06$X$\u6620\u5c04\u5230$Y$\u7684\u6ee1\u5c04, \u82e5$V$\u662f$Y$\u4e2d\u7684\u5f00\u96c6\u5f53\u4e14\u4ec5\u5f53$f^{-1}(V)$\u662f$X$\u4e2d\u7684\u5f00\u96c6, \u5219\u79f0$f$\u662f\u4e00\u4e2a\u5c06$X$\u6620\u5c04\u5230$Y$\u7684\u5546\u6620\u5c04. \u663e\u7136, $f(f^{-1}(V)) = $$ V$\u662f\u6210\u7acb\u7684, \u56e0\u4e3a$f$\u662f\u4e00\u4e2a\u6ee1\u5c04. \u4f46\u7531\u4e8e\u5728$X$\u4e2d\u5e76\u975e\u6240\u6709\u5f00\u96c6\u90fd\u53ef\u4ee5\u5199\u6210$f^{-1}(V), V \\subset Y$\u7684\u5f62\u5f0f, \u6545\u5546\u6620\u5c04\u5e76\u4e0d\u4e00\u5b9a\u662f\u4e00\u4e2a\u5f00\u6620\u5c04\u6216\u8005\u95ed\u6620\u5c04.<\/p>\n<p><strong>2. \u5546\u7a7a\u95f4\u4e2d\u7684\u5b50\u96c6\u5f00\u5f53\u4e14\u4ec5\u5f53\u5176\u5173\u4e8e\u7c98\u5408\u6620\u5c04\u7684\u539f\u50cf\u5f00. \u6362\u8a00\u4e4b, \u7c98\u5408\u6620\u5c04\u662f\u5546\u6620\u5c04.<\/strong><\/p>\n<p><strong>3. \u7c98\u5408\u6620\u5c04\u7684\u590d\u5408\u6620\u5c04\u8fd8\u662f\u4e00\u4e2a\u7c98\u5408\u6620\u5c04, \u7c98\u5408\u6620\u5c04\u7684\u987a\u5e8f\u5728\u540c\u80da\u610f\u4e49\u4e0a\u4e0d\u5f71\u54cd\u6700\u7ec8\u7684\u7c98\u5408\u7ed3\u679c.<\/strong><\/p>\n<p>\u8fd9\u4e2a\u547d\u9898\u7684\u76f4\u89c2\u8bc1\u660e\u53ef\u4ee5\u53c2\u8003\u5e84\u6653\u6ce2\u8001\u5e08\u7684\u57fa\u7840\u62d3\u6251\u5b66\u9891\u9053\u7684P22\u6559\u7a0b(\u8001\u5e08\u5728\u89c6\u9891\u8d77\u59cb\u5904\u4fbf\u8ba8\u8bba\u8fd9\u4e2a\u95ee\u9898).<\/p>\n<p><strong>4. \u8fdb\u884c\u7c98\u5408\u6620\u5c04\u65f6\u5bf9\u5f84\u70b9\u662f\u6839\u636e\u7c98\u5408\u65b9\u5411\u53d8\u52a8\u7684.<\/strong><\/p>\n<p>\u5982\u4e0b\u56fe\u5c55\u793a\u4e86\u4e24\u79cd\u4e0d\u540c\u65b9\u5411\u7684\u5bf9\u5f84\u70b9, $A$\u4e0e$A&#8217;$, $B$\u4e0e$B&#8217;$\u5206\u522b\u8868\u793a\u4e24\u5bf9\u5bf9\u5f84\u70b9, \u5bf9\u5f84\u70b9\u4f1a\u88ab\u7c98\u5408\u6620\u5c04\u6620\u5c04\u5230\u540c\u4e00\u70b9\u4e0a.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/\u7c98\u5408\u6620\u5c04\u5bf9\u5f84\u70b9\u793a\u610f\u56fe.png\" alt=\"\" width=\"1820\" height=\"792\" class=\"alignnone size-full wp-image-976\" srcset=\"https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/\u7c98\u5408\u6620\u5c04\u5bf9\u5f84\u70b9\u793a\u610f\u56fe.png 1820w, https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/\u7c98\u5408\u6620\u5c04\u5bf9\u5f84\u70b9\u793a\u610f\u56fe-300x131.png 300w, https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/\u7c98\u5408\u6620\u5c04\u5bf9\u5f84\u70b9\u793a\u610f\u56fe-768x334.png 768w, https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/\u7c98\u5408\u6620\u5c04\u5bf9\u5f84\u70b9\u793a\u610f\u56fe-1536x668.png 1536w\" sizes=\"(max-width: 1820px) 100vw, 1820px\" \/><\/p>\n<p>\u603b\u7684\u6765\u8bf4, \u7c98\u5408\u6620\u5c04\u662f\u4e00\u4e2a\u975e\u5e38\u6709\u610f\u601d\u7684\u6620\u5c04, \u91cc\u9762\u7684\u4f8b\u5b50\u90fd\u503c\u5f97\u5b66\u4e60\u4e00\u6ce2~ \u4e0b\u56fe\u5217\u51fa\u4e86\u4e00\u4e9b\u5e38\u89c1\u7684\u7c98\u5408\u65b9\u5f0f\u53ca\u7c98\u5408\u540e\u6240\u5f97\u7684\u7a7a\u95f4:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/v2-cecc28916c957b9f15345b98565aaf9b_b.jpg\" alt=\"\" width=\"720\" height=\"965\" class=\"alignnone size-full wp-image-977\" srcset=\"https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/v2-cecc28916c957b9f15345b98565aaf9b_b.jpg 720w, https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/v2-cecc28916c957b9f15345b98565aaf9b_b-224x300.jpg 224w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/p>\n<p style=\"text-align: center;\">(\u56fe\u7247\u6765\u6e90: <a href=\"https:\/\/zhuanlan.zhihu.com\/p\/147532659\">\u95ed\u66f2\u9762\u7684\u5206\u7c7b\u53ca\u66f2\u9762\u7684\u4e09\u89d2\u5256\u5206<\/a>)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u5468\u5468\u672b\u522e\u53f0\u98ce, \u6240\u4ee5\u53ea\u80fd&#8221;\u88ab\u8feb&#8221;\u5446\u5728\u5bb6\u91cc2333 \u8fd9\u5468\u4e3b\u8981\u9488\u5bf9\u7c98\u5408\u6620\u5c04\u7684\u90e8\u5206\u4f5c\u4e86\u4e00\u4e9b &hellip; <a href=\"https:\/\/www.caiqinyi.cn\/index.php\/2021\/07\/25\/gluing_map\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u7c98\u5408\u6620\u5c04<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"_links":{"self":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/967"}],"collection":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/comments?post=967"}],"version-history":[{"count":16,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/967\/revisions"}],"predecessor-version":[{"id":3629,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/967\/revisions\/3629"}],"wp:attachment":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/media?parent=967"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/categories?post=967"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/tags?post=967"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}