{"id":884,"date":"2021-06-17T11:46:55","date_gmt":"2021-06-17T03:46:55","guid":{"rendered":"https:\/\/www.caiqinyi.cn\/?p=884"},"modified":"2022-10-21T16:20:17","modified_gmt":"2022-10-21T08:20:17","slug":"manifold_regular_space","status":"publish","type":"post","link":"https:\/\/www.caiqinyi.cn\/index.php\/2021\/06\/17\/manifold_regular_space\/","title":{"rendered":"\u6d41\u5f62\u662f\u6b63\u5219\u7a7a\u95f4\u7684\u8bc1\u660e"},"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\u8981\u5f00\u59cb\u82e6\u903c\u7684996\u52a0\u73ed\u751f\u6d3b\u4e86, \u6628\u5929\u7248\u672c\u65e5\u52a0\u73ed\u523012\u70b9, \u6240\u4ee5\u4eca\u5929\u4e0a\u5348\u8bf7\u4e86\u4e2a\u5047, \u6bd5\u7adf\u8fd8\u662f\u5f97\u4ece\u81ea\u5df1\u7684\u8eab\u4f53\u51fa\u53d1\u4e3a\u81ea\u5df1\u8003\u8651, \u4e3a\u516c\u53f8\u62fc\u547d\u600e\u4e48\u60f3\u90fd\u662f\u4e0d\u503c\u5f97\u7684. \u4ece\u8fd9\u5468\u5f00\u59cb, \u81ea\u5df1\u4e5f\u60f3\u7740\u575a\u6301\u6bcf\u5468\u90fd\u8d77\u7801\u66f4\u65b0\u4e00\u7bc7\u6587\u7ae0, \u7528\u4ee5\u8bb0\u5f55\u5f53\u5468\u5b66\u4e60\u62d3\u6251\u7684\u8fc7\u7a0b\u4e2d\u5b66\u61c2\u7684\u4e00\u4e2a\u5c0f\u77e5\u8bc6\u70b9. \u8bdd\u4e0d\u591a\u8bf4, \u8fdb\u5165\u6b63\u9898~<\/p>\n<p><!--more--><\/p>\n<p>\u8bc1\u660e\u6d41\u5f62$X$\u662f\u6b63\u5219\u7a7a\u95f4, \u5373\u4efb\u53d6$x \\in X$\u53ca\u5176\u5f00\u90bb\u57df$U$, \u5b58\u5728$x$\u7684\u5f00\u90bb\u57df$V$\u4f7f\u5f97$\\bar{V} $$ \\subseteq U$.<br \/>\n$\\\\$ <strong>\u8bc1:<\/strong> \u7531\u6d41\u5f62\u7684\u5b9a\u4e49\u77e5\u4efb\u53d6$x \\in X$\u90fd\u5b58\u5728\u5f00\u90bb\u57df$W$\u540c\u80da\u4e8e$E_n$, \u53c8$E_n$\u662f\u4e00\u4e2a\u6b63\u5219\u7a7a\u95f4, \u5219$x$\u5728\u8be5\u540c\u80da\u6620\u5c04\u4e0b\u7684\u50cf\u70b9$y$\u5728$E_n$\u4e2d\u4efb\u53d6\u5f00\u90bb\u57df\u90fd\u5305\u542b$y$\u7684\u4e00\u4e2a\u5f00\u90bb\u57df\u7684\u95ed\u5305. \u4ece\u800c\u7531\u540c\u80da\u7684\u6027\u8d28\u77e5(\u597d\u5427, \u6211\u627f\u8ba4\u8fd9\u4e00\u5757\u8bc1\u660e\u5f88\u7275\u5f3a\u2026\u2026), $x \\in X$, \u4e5f\u5b58\u5728\u5f00\u90bb\u57df$U$\u4f7f\u5f97$\\bar{V} \\subseteq  U$, \u5176\u4e2d$V$\u662f$x$\u7684\u5f00\u90bb\u57df. \u7efc\u4e0a\u6240\u8ff0, \u547d\u9898\u5f97\u8bc1.<\/p>\n<p>PS: \u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\u662f\u9700\u8981\u8bc1\u660e\u7d27\u81f4\u6d41\u5f62$M$\u662f\u4e00\u4e2a\u7b2c\u4e8c\u53ef\u6570\u7a7a\u95f4. \u8bc1\u660e\u601d\u8def\u662f\u5229\u7528\u7d27\u81f4\u6027\u63a8\u51fa$M$\u53ef\u4ee5\u88ab\u6709\u9650\u4e2a\u5f00\u96c6$\\{U_i\\}$\u8986\u76d6, \u4f7f\u5f97\u6bcf\u4e2a$U_i$\u90fd\u80fd\u591f\u540c\u80da\u4e8e$E_n$, \u8fd9\u4e2a\u63a8\u65ad\u786e\u5b9e\u5177\u5907\u51e0\u4f55\u76f4\u89c2\u6027, \u4f46\u4e25\u683c\u7684\u8bc1\u660e\u6211\u8fd8\u662f\u6ca1\u60f3\u51fa\u6765, \u53ef\u80fd\u9700\u8981\u57fa\u672c\u7fa4\u7684\u77e5\u8bc6\u6765\u89e3\u51b3\u53ed=.=<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u5468\u8981\u5f00\u59cb\u82e6\u903c\u7684996\u52a0\u73ed\u751f\u6d3b\u4e86, \u6628\u5929\u7248\u672c\u65e5\u52a0\u73ed\u523012\u70b9, \u6240\u4ee5\u4eca\u5929\u4e0a\u5348\u8bf7\u4e86\u4e2a\u5047, \u6bd5\u7adf\u8fd8\u662f\u5f97\u4ece\u81ea\u5df1\u7684\u8eab\u4f53\u51fa &hellip; <a href=\"https:\/\/www.caiqinyi.cn\/index.php\/2021\/06\/17\/manifold_regular_space\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u6d41\u5f62\u662f\u6b63\u5219\u7a7a\u95f4\u7684\u8bc1\u660e<\/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\/884"}],"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=884"}],"version-history":[{"count":16,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/884\/revisions"}],"predecessor-version":[{"id":2567,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/884\/revisions\/2567"}],"wp:attachment":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/media?parent=884"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/categories?post=884"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/tags?post=884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}