{"id":1141,"date":"2021-10-03T18:37:24","date_gmt":"2021-10-03T10:37:24","guid":{"rendered":"https:\/\/www.caiqinyi.cn\/?p=1141"},"modified":"2025-02-26T11:17:44","modified_gmt":"2025-02-26T03:17:44","slug":"deformation_retraction_mark","status":"publish","type":"post","link":"https:\/\/www.caiqinyi.cn\/index.php\/2021\/10\/03\/deformation_retraction_mark\/","title":{"rendered":"\u5f62\u53d8\u6536\u7f29\u6ce8\u8bb0"},"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>\u4eca\u5e74\u7684\u56fd\u5e86\u5047\u671f\u4f9d\u65e7\u662f\u5728\u5bb6\u4e2d\u5ea6\u8fc7\u7684, \u611f\u89c9\u5f88\u4e0d\u9519, \u53c8\u662f\u4e00\u4e2a\u53ef\u4ee5\u5728\u5bb6\u91cc\u5b85\u723d\u4e00\u5468\u7684\u5047\u671fhhh~ \u56de\u5230\u5bb6\u91cc\u7684\u8fd9\u51e0\u5929\u4e3b\u8981\u7cbe\u529b\u90fd\u653e\u5728\u4e86\u5085\u5b5d\u660e\u8001\u5e08\u7684\u6570\u5b57\u51e0\u4f55\u5904\u7406\u7f51\u8bfe\u4e0a, \u4ee3\u6570\u62d3\u6251\u7684\u5b66\u4e60\u53cd\u800c\u6709\u70b9\u677e\u61c8\u4e86, \u63a5\u4e0b\u6765\u7684\u51e0\u5929\u5047\u671f\u7684\u5b66\u4e60\u8ba1\u5212\u9700\u8981\u597d\u597d\u8c03\u6574\u4e00\u4e0b. \u672c\u6587\u4e3b\u8981\u662f\u8bb0\u5f55\u5f62\u53d8\u6536\u7f29\u8fd9\u4e00\u5757\u77e5\u8bc6\u70b9\u7684\u76f8\u5173\u7b14\u8bb0~<\/p>\n<p><!--more--><\/p>\n<p><strong>\u53c2\u8003\u6750\u6599<\/strong><br \/>\n1. <a href=\"https:\/\/www.zhihu.com\/question\/471513639\/answer\/1992077898\">\u5982\u4f55\u8bc1\u660eA\u4e0d\u662fX\u7684\u5f3a\u5f62\u53d8\u6536\u7f29\u6838\uff1f<\/a><br \/>\n2. <a href=\"https:\/\/www.zhihu.com\/question\/59893822\/answer\/173316657\">\u5982\u4f55\u76f4\u89c2\u5730\u533a\u5206\u6536\u7f29\u6838\uff0c\u5f62\u53d8\u6536\u7f29\u6838\uff0c\u5f3a\u5f62\u53d8\u6536\u7f29\u6838\uff1f<\/a><\/p>\n<p><strong>1. \u4f26\u79fb\u7684\u76f4\u89c2\u89e3\u91ca<\/strong><\/p>\n<p>\u5728\u5f88\u591a\u62d3\u6251\u7684\u79d1\u666e\u6587\u91cc, \u901a\u5e38\u4f1a\u628a\u540c\u80da\u63cf\u7ed8\u6210&#8221;\u4e00\u4e2a\u634f\u6a61\u76ae\u6ce5\u7684\u8fc7\u7a0b&#8221;. \u79c1\u4ee5\u4e3a, \u8fd9\u662f\u6bd4\u8f83\u7247\u9762\u7684\u4e00\u79cd\u8bf4\u6cd5: \u9996\u5148, \u540c\u80da\u53ea\u662f\u4e00\u4e2a\u6620\u5c04\u800c\u975e\u9010\u6e10\u53d8\u5f62\u7684\u8fc7\u7a0b; \u5176\u6b21, \u540c\u80da\u53ea\u662f\u540c\u4f26\u7b49\u4ef7\u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u5f62. \u76f8\u6bd4\u8f83\u540c\u80da, \u4f26\u79fb\u7684\u6982\u5ff5\u66f4\u50cf\u662f\u63cf\u8ff0&#8221;\u9010\u6e10\u53d8\u5f62\u7684\u8fc7\u7a0b&#8221;\u7684\u672f\u8bed. \u4e0e\u4e4b\u76f8\u5e94\u7684, \u6709\u4e00\u4e2a\u63cf\u8ff0\u4e24\u4e2a\u62d3\u6251\u7a7a\u95f4&#8221;\u8fde\u7eed\u53d8\u5f62&#8221;\u7684\u72b6\u6001\u7684\u672f\u8bed, \u8fd9\u4fbf\u662f\u540c\u4f26\u7b49\u4ef7.<\/p>\n<p><strong>2. \u5e9e\u52a0\u83b1\u731c\u60f3<\/strong><\/p>\n<p>\u76ee\u524d\u6211\u6240\u4e86\u89e3\u5230\u7684\u540c\u4f26\u7b49\u4ef7\u7684\u4f5c\u7528, \u4fbf\u662f\u5728\u8ba1\u7b97\u57fa\u672c\u7fa4\u65f6\u7b80\u5316\u8ba1\u7b97, \u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u628a\u4e00\u4e2a\u76f8\u5bf9\u590d\u6742\u7684\u539f\u59cb\u7a7a\u95f4\u540c\u4f26\u7b49\u4ef7\u5230\u4e00\u4e2a\u76f8\u5bf9\u7b80\u5355\u7684\u5f62\u72b6, \u7136\u540e\u518d\u8fdb\u884c\u57fa\u672c\u7fa4\u7684\u8ba1\u7b97. \u4f46\u662f, \u8fd9\u4e2a\u6280\u5de7\u4e5f\u6709\u4e00\u4e2a\u7f3a\u70b9: \u5982\u679c\u4e24\u4e2a\u7a7a\u95f4\u540c\u4f26\u7b49\u4ef7, \u90a3\u6211\u4eec\u4e60\u5f97\u7684\u5f88\u591a\u4ee3\u6570\u62d3\u6251\u5de5\u5177\u5c06\u5f88\u96be\u533a\u5206\u5b83\u4eec. \u5e9e\u52a0\u83b1\u5728\u53d1\u660e\u57fa\u672c\u7fa4\u7684\u65f6\u5019\u5c31\u66fe\u7ecf\u63d0\u51fa\u8fc7\u8fd9\u6837\u4e00\u4e2a\u731c\u60f3: \u5982\u679c\u4e00\u4e2a\u95ed\u4e09\u7ef4\u6d41\u5f62$X$\u7684\u57fa\u672c\u7fa4\u548c\u4e09\u7ef4\u7403\u9762$S^2$\u7684\u57fa\u672c\u7fa4\u4e00\u6837\u5e73\u51e1, \u662f\u5426\u80fd\u80af\u5b9a$X$\u540c\u80da\u4e8e$S^3$? \u56e0\u4e3a\u7531\u95ed\u66f2\u9762\u5206\u7c7b\u5b9a\u7406\u53ef\u77e5\u57fa\u672c\u7fa4\u5e73\u51e1\u7684\u95ed\u66f2\u9762\u4e00\u5b9a\u540c\u80da\u4e8e$S^2$, \u6240\u4ee5\u5e9e\u52a0\u83b1\u5927\u80c6\u5730\u8ba4\u4e3a\u8be5\u731c\u60f3\u5728\u4e09\u7ef4\u60c5\u5f62\u4e0b\u4e5f\u80fd\u6210\u7acb, \u8fd9\u4fbf\u662f\u8457\u540d\u7684\u5e9e\u52a0\u83b1\u731c\u60f3.<br \/>\n$\\\\$ \u5f53\u7136, \u5e9e\u52a0\u83b1\u731c\u60f3\u60ac\u800c\u672a\u51b3\u7684\u65f6\u95f4\u957f\u8fbe\u534a\u4e2a\u591a\u4e16\u7eaa, \u76f4\u52301960\u5e74Smale\u624d\u7a81\u7136\u53d1\u73b0\u5b83\u7684\u9ad8\u7ef4\u63a8\u5e7f\u4f3c\u4e4e\u66f4\u5bb9\u6613\u8bc1\u660e\u4e00\u4e9b, \u5e76\u8bc1\u660e\u4e86$n \\ge 5$\u7684\u60c5\u5f62; \u800c\u76f4\u52302006\u5e74, \u5e9e\u52a0\u83b1\u731c\u60f3\u624d\u88ab\u4fc4\u56fd\u6570\u5b66\u5bb6\u4f69\u96f7\u5c14\u66fc\u6700\u7ec8\u89e3\u51b3.<\/p>\n<p><strong>3. \u5f62\u53d8\u6536\u7f29<\/strong><\/p>\n<p>\u5148\u6765\u770b\u770b\u5f62\u53d8\u6536\u7f29\u7684\u5b9a\u4e49: \u8bbe$A \\subseteq X$, $i : A \\hookrightarrow X$\u662f\u5305\u542b\u6620\u5c04. \u5982\u679c\u6620\u5c04$r : X $$ \\to A$\u6ee1\u8db3$r \\circ i = r|_A = id_A$, \u5219\u79f0\u4e4b\u4e3a\u6536\u7f29\u6620\u5c04, \u79f0$A$\u4e3a$X$\u7684\u6536\u7f29\u6838. \u5982\u679c\u4e00\u4e2a\u6536\u7f29\u6620\u5c04$r$\u8fd8\u6ee1\u8db3$i \\circ r \\cong id_X$, \u5219\u79f0\u4e4b\u4e3a\u5f62\u53d8\u6536\u7f29, \u79f0$A$\u4e3a$X$\u7684\u5f62\u53d8\u6536\u7f29\u6838. \u5982\u679c\u5f62\u53d8\u6536\u7f29$r$\u8fd8\u6ee1\u8db3$i \\circ r \\cong<br \/>\n $$ id_X\\ rel\\ A$, \u5219\u79f0\u4e4b\u4e3a\u5f3a\u5f62\u53d8\u6536\u7f29, \u79f0$A$\u4e3a$X$\u7684\u5f3a\u5f62\u53d8\u6536\u7f29\u6838.<br \/>\n$\\\\$ \u8fd9\u4e00\u4e32\u5b9a\u4e49\u770b\u8d77\u6765\u5f88\u5197\u957f\u4e14\u62bd\u8c61, \u5176\u5b9e\u4ed4\u7ec6\u601d\u8003\u4ee5\u540e\u4e5f\u4e0d\u96be\u7406\u89e3. \u540e\u9762\u4e00\u4e2a\u6982\u5ff5\u603b\u662f\u5728\u524d\u9762\u4e00\u4e2a\u6982\u5ff5\u7684\u57fa\u7840\u4e4b\u4e0a\u6dfb\u52a0\u4e86\u67d0\u4e9b\u6761\u4ef6\u5b9a\u4e49\u5f97\u5230\u7684. \u9700\u8981\u6ce8\u610f\u7684\u662f, \u6536\u7f29\u6620\u5c04\u7684\u5b9a\u4e49\u4e2d, $r \\circ i$\u662f\u4e0e$id_A$\u76f8\u7b49\u7684, \u800c\u5728\u5b9a\u4e49\u4e2d, \u5219\u8fd8\u8981\u6c42$i \\circ r$\u4e0e$id_X$\u540c\u4f26; \u800c\u5f53\u8ba8\u8bba\u5f3a\u5f62\u53d8\u6536\u7f29\u65f6, \u5219\u9700\u6ce8\u610f, \u5728&#8221;\u6536\u7f29&#8221;\u8fc7\u7a0b\u4e2d, \u82e5$X$\u7684\u5b50\u96c6$A$\u4e2d\u7684\u70b9\u7684&#8221;\u4f4d\u7f6e&#8221;\u59cb\u7ec8\u4fdd\u6301\u4e0d\u53d8, \u5219\u79f0\u5b50\u96c6$A$\u4e3a$X$\u7684\u5f3a\u5f62\u53d8\u6536\u7f29\u6838.<br \/>\n$\\\\$ \u53ef\u4ee5\u770b\u51fa, \u5f62\u53d8\u6536\u7f29\u662f\u4e00\u7c7b\u7279\u6b8a\u7684\u540c\u4f26\u7b49\u4ef7: \u5982\u679c$r$\u662f\u5f62\u53d8\u6536\u7f29, \u5219$r$\u548c$i$\u4e92\u4e3a\u540c\u4f26\u9006, \u4f46\u5f62\u53d8\u6536\u7f29\u8981\u6bd4\u4e00\u822c\u7684\u540c\u4f26\u7b49\u4ef7\u76f4\u89c2\u5f97\u591a. \u56e0\u6b64, \u6211\u4eec\u7ecf\u5e38\u5728\u4e00\u4e9b\u76f8\u5173\u4f8b\u5b50\u4e2d\u53ef\u4ee5\u770b\u5230&#8221;\u6253\u6d1e&#8221;\u7684\u64cd\u4f5c, \u6765\u628a\u67d0\u4e2a\u62d3\u6251\u7a7a\u95f4\u6536\u7f29\u5230\u53e6\u5916\u4e00\u4e2a\u62d3\u6251\u7a7a\u95f4\u4e2d, \u5b83\u4eec\u662f\u540c\u4f26\u7b49\u4ef7\u7684, \u8fd9\u6837\u4fbf\u53ef\u4ee5\u7b80\u5316\u4e00\u4e9b\u57fa\u672c\u7fa4\u7b49\u7684\u8ba1\u7b97. <\/p>\n<p><strong>4. \u540c\u4f26\u7684\u590d\u5408\u8fd0\u7b97\u7684\u76f8\u5173\u5f15\u7406<\/strong><\/p>\n<p>\u7ecf\u5e38\u53ef\u4ee5\u770b\u5230\u5728\u4e00\u4e9b\u540c\u4f26\u547d\u9898\u7684\u76f8\u5173\u8bc1\u660e\u4e2d, \u76f4\u63a5\u5c31\u7528\u5230\u4e86\u4e0b\u9762\u7684\u5f15\u7406, \u53ef\u4ee5\u6781\u5927\u5730\u7b80\u5316\u540c\u4f26\u7684\u590d\u5408\u8fd0\u7b97.<\/p>\n<p><strong>\u5f15\u7406<\/strong> \u82e5$X \\overset{f}{\\rightarrow} Y \\overset{h_1, h_2}{\\longrightarrow} Z \\overset{g}{\\rightarrow} W$, \u4e14$h_1 \\cong h_2$, \u5219$h_1 \\circ f \\cong h_2 \\circ f$, $g \\circ h_1 \\cong g $$ \\circ h_2$.<br \/>\n$\\\\$ \u8fd9\u4e2a\u5f15\u7406\u76f4\u63a5\u5229\u7528\u540c\u4f26\u7684\u5b9a\u4e49\u5373\u53ef\u8bc1.<\/p>\n<p><strong>5. \u5f3a\u5f62\u53d8\u6536\u7f29\u76f8\u5173\u4e60\u9898<\/strong><\/p>\n<p><strong>\u547d\u9898<\/strong> \u4ee4$X= \\{ (x, y) \\in E^2 | x \\in Q \\ or \\ y = 0 \\}$, \u8bc1\u660e$(0, 1)$\u4e0d\u662f$X$\u7684\u5f3a\u5f62\u53d8\u6536\u7f29\u6838.<br \/>\n$\\\\$ <strong>\u8bc1:<\/strong> \u53ef\u4ee5\u5148\u76f4\u89c2\u4e0a\u6765\u7406\u89e3\u4e00\u4e0b\u8fd9\u4e2a\u547d\u9898: \u5982\u679c$(0, 1)$\u4fdd\u6301\u4e0d\u52a8, \u90a3\u4e48\u5de6\u53f3\u4e24\u8fb9\u7684\u70b9\u59cb\u7ec8\u5904\u4e8e\u9644\u8fd1, \u4f46\u662f\u5de6\u53f3\u4e24\u8fb9\u7684\u70b9\u8981\u6536\u7f29\u5230$(0, 1)$\u5c31\u5fc5\u987b\u7ecf\u8fc7$x$\u8f74.<br \/>\n$\\\\$ \u91c7\u7528\u53cd\u8bc1\u6cd5, \u5047\u8bbe$(0, 1)$\u662f$X$\u7684\u5f3a\u5f62\u53d8\u6536\u7f29\u6838, $H : X \\times I \\to X$\u4e3a\u76f8\u5e94\u7684\u5f3a\u5f62\u53d8\u6536\u7f29\u6620\u5c04, \u5176\u4e2d$I = [0, 1]$. \u53d6\u5b9a$$U = \\{ (x, y) \\in X | y > 0 \\},$$\u7531<a href=\"https:\/\/en.wikipedia.org\/wiki\/Tube_lemma\">Tube\u5f15\u7406<\/a>\u53ef\u77e5\u5b58\u5728$(0, 1)$\u7684\u90bb\u57df$V \\subseteq U$. \u4e0d\u5931\u4e00\u822c\u6027\u5730, \u6211\u4eec\u53ef\u4ee5\u4ee4$$V = \\{ (\\frac{1}{n}, y) \\in X | n = 1, 2, \\cdots, 0 \\le y \\le 1 \\} \\cup ({0} \\times I),$$\u5219$V$\u4e3a$X$\u7684\u7d27\u5b50\u96c6. \u7531\u5eb7\u6258\u4e00\u81f4\u6027\u5b9a\u7406\u53ef\u77e5$H$\u9650\u5236\u5728$V \\times I$\u4e0a\u662f\u4e00\u81f4\u8fde\u7eed\u7684.<br \/>\n$\\\\$ \u6545$\\exists \\delta > 0$, s.t. $d((x_1, y_1, t_1), (x_2, y_2, t_2)) < \\delta$, $(x_1, y_1, t_1)$, $(x_2, $$ y_2, t_2) \\in $$ V \\times I $$ \\Rightarrow d(H((x_1, y_1, t_1)), H((x_2, y_2, t_2))) < 1\/2$, \u5176\u4e2d, $d$\u4e3a\u4e00\u822c\u7684\u6b27\u6c0f\u8ddd\u79bb.\n<br \/>\n$\\\\$ \u53d6\u5145\u5206\u5927\u7684\u81ea\u7136\u6570$n$\u4f7f\u5f97$1\/n < \\delta$. \u7531\u4e8e\u539f\u70b9$(0, 0)$\u662f$V$\u7684\u4e00\u4e2a\u5206\u5272\u70b9, \u5373\u53bb\u6389$(0, 0)$\u4ee5\u540e$V$\u80fd\u591f\u88ab\u5206\u89e3\u6210\u4e24\u4e2a\u975e\u7a7a\u5f00\u96c6\u7684\u5e76\u96c6, \u6545\u7531\u4ecb\u503c\u5b9a\u7406\u53ef\u77e5\u5b58\u5728\u4e00\u4e2a\u65f6\u95f4$t_0$\u4f7f\u5f97$H(1\/n, 1, t_0) = (0, 0)$. \u800c\u7531\u4e8e$H$\u662f\u4e00\u4e2a\u5f3a\u5f62\u53d8\u6536\u7f29, $H(0, 1, t_0) = $$ (0, 1)$, \u4ece\u800c$(1\/n, 1, t_0)$, $(0, 1, $$ t_0)$\u4e4b\u95f4\u7684\u8ddd\u79bb\u5c0f\u4e8e$\\delta$. \u7136\u800c$$d(H((1\/n, 1, t_0)),H((0, 1, t_0))) \\\\ = d((0, 0), (0, 1)) = 1 > 1\/2,$$\u4ea7\u751f\u77db\u76fe, \u6545\u547d\u9898\u5f97\u8bc1.<br \/>\n<\/p>\n<p>PS: \u82e5\u8981\u8bc1\u660e\u4e24\u4e2a\u62d3\u6251\u7a7a\u95f4\u4e0d\u540c\u80da, \u6709\u4e00\u4e2a\u5f88\u53d6\u5de7\u7684\u505a\u6cd5\u662f: \u5206\u522b\u4ece\u4e24\u4e2a\u62d3\u6251\u7a7a\u95f4\u4e2d&#8221;\u6316&#8221;\u53bb\u4e00\u70b9, \u7136\u540e\u8003\u5bdf\u4e24\u4e2a\u4f59\u96c6\u7684\u8fde\u901a\u6027\u5373\u53ef, \u4f46&#8221;\u6316&#8221;\u53bb\u7684\u70b9\u4e0d\u662f\u4efb\u610f\u7684, \u8bc1\u660e\u7684\u8bed\u8a00\u5e94\u8be5\u4e25\u8c28, \u4e0b\u9762\u662f\u4e00\u4e2a\u53cd\u4f8b.<\/p>\n<p><strong>\u547d\u9898<\/strong> \u8bbe$X$\u662f\u4e24\u4e2a\u76f8\u5207\u7684\u5706\u5468\u7684\u5e76\u96c6, $Y$\u662f\u4e00\u4e2a\u6b63\u65b9\u5f62\u7684\u56db\u6761\u8fb9\u52a0\u4e0a\u4e00\u6761\u5bf9\u89d2\u7ebf\u7684\u5e76\u96c6, \u8bc1\u660e$X$\u548c$Y$\u4e0d\u540c\u80da.<br \/>\n$\\\\$ <strong>\u8bef\u8bc1:<\/strong> $X$\u53bb\u6389\u5207\u70b9\u540e\u6709\u4e24\u4e2a\u5206\u652f, \u800c$Y$\u53bb\u6389\u4e00\u70b9\u540e\u4ecd\u7136\u8fde\u901a.<br \/>\n$\\\\$ \u6b64\u5904\u8bc1\u660e\u7684\u51fa\u53d1\u70b9\u662f\u5bf9\u7684, \u4f46\u8bed\u8a00\u4e0d\u591f\u4e25\u8c28, \u5bb9\u6613\u4ea7\u751f\u6b67\u4e49, \u56e0\u4e3a\u6211\u4eec\u4ec5\u9700\u8981\u8003\u8651$Y$\u4e2d\u53bb\u6389\u4e00\u4e2a\u7279\u6b8a\u70b9\u540e\u7684\u8fde\u901a\u6027\u5373\u53ef, \u6b63\u786e\u8bc1\u660e\u5982\u4e0b\u6240\u793a.<\/p>\n<p><strong>\u8bc1:<\/strong> \u5047\u8bbe\u5b58\u5728\u540c\u80da$f:X  \\longrightarrow Y$, \u8bb0$x$\u4e3a$X$\u7684\u5207\u70b9, \u8bbe$f(x)=y$, \u5219$f$\u8bf1\u5bfc$X \\backslash \\{ $$ x \\}$\u5230$Y \\backslash \\{ y \\}$\u7684\u540c\u80da. \u53c8$X \\backslash \\{ x \\}$\u6709\u4e24\u4e2a\u5206\u652f, $Y \\backslash \\{ y \\}$\u8fde\u901a. \u800c\u8fde\u901a\u6027\u662f\u4e00\u79cd\u62d3\u6251\u6027\u8d28, \u8fd9\u4e2a\u77db\u76fe\u5c31\u8bf4\u660e\u5047\u8bbe\u9519\u8bef, \u5373$X$\u548c$Y$\u4e0d\u540c\u80da.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4eca\u5e74\u7684\u56fd\u5e86\u5047\u671f\u4f9d\u65e7\u662f\u5728\u5bb6\u4e2d\u5ea6\u8fc7\u7684, \u611f\u89c9\u5f88\u4e0d\u9519, \u53c8\u662f\u4e00\u4e2a\u53ef\u4ee5\u5728\u5bb6\u91cc\u5b85\u723d\u4e00\u5468\u7684\u5047\u671fhhh~ \u56de\u5230\u5bb6\u91cc\u7684\u8fd9\u51e0\u5929\u4e3b &hellip; <a href=\"https:\/\/www.caiqinyi.cn\/index.php\/2021\/10\/03\/deformation_retraction_mark\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u5f62\u53d8\u6536\u7f29\u6ce8\u8bb0<\/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\/1141"}],"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=1141"}],"version-history":[{"count":33,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/1141\/revisions"}],"predecessor-version":[{"id":3628,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/1141\/revisions\/3628"}],"wp:attachment":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}