{"id":425,"date":"2025-07-12T14:40:19","date_gmt":"2025-07-12T13:40:19","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=425"},"modified":"2025-07-12T14:40:19","modified_gmt":"2025-07-12T13:40:19","slug":"teorema-del-punt-fix-de-brouwer-i-aplicacions","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/teorema-del-punt-fix-de-brouwer-i-aplicacions\/","title":{"rendered":"Teorema del punt fix de Brouwer i aplicacions"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p>El <strong>teorema del punt fix de Brouwer<\/strong> estableix que tota funci\u00f3 cont\u00ednua des d&#8217;una bola tancada d&#8217;un espai euclidi\u00e0 cap a si mateixa t\u00e9 un punt fix. Aquest teorema va estimular el naixement de la <strong>topologia algebraica<\/strong> i t\u00e9 aplicacions importants en <strong>teoria de jocs i economia<\/strong>. Aquest treball t\u00e9 com a objectiu d&#8217;estudiar algunes demostracions del teorema de Brouwer, i d&#8217;explorar diverses aplicacions del teorema, com ara en teoria de jocs amb el <strong>teorema d&#8217;Hex<\/strong> o en topologia amb el <strong>teorema de Jordan<\/strong>.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Bibliografia orientativa<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>The Game of Hex and the Brouwer Fixed-Point Theorem<\/em> &#8211; David Gale. <\/li>\n\n\n\n<li><em>The Jordan Curve Theorem Via the Brouwer Fixed Point Theorem<\/em> &#8211; Ryuji Maehara<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>El teorema del punt fix de Brouwer estableix que tota funci\u00f3 cont\u00ednua des d&#8217;una bola tancada d&#8217;un espai euclidi\u00e0 cap a si mateixa t\u00e9 un punt fix. Aquest teorema va estimular el naixement de la topologia algebraica i t\u00e9 aplicacions importants en teoria de jocs i economia. Aquest treball t\u00e9 com a objectiu d&#8217;estudiar algunes [&hellip;]<\/p>\n","protected":false},"author":75,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[44],"class_list":["post-425","post","type-post","status-publish","format-standard","hentry","category-geometria-i-topologia","tag-florent-balacheff"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/425","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/75"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=425"}],"version-history":[{"count":7,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/425\/revisions"}],"predecessor-version":[{"id":433,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/425\/revisions\/433"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=425"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=425"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}