{"id":94076,"date":"2018-03-11T10:13:41","date_gmt":"2018-03-11T10:13:41","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/semi-lipschitz-functions-best-approximation-and-fuzzy-quasi-metric-hyperspaces\/"},"modified":"2018-03-11T10:13:41","modified_gmt":"2018-03-11T10:13:41","slug":"semi-lipschitz-functions-best-approximation-and-fuzzy-quasi-metric-hyperspaces","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/semi-lipschitz-functions-best-approximation-and-fuzzy-quasi-metric-hyperspaces\/","title":{"rendered":"Semi-lipschitz functions, best approximation, and fuzzy quasi-metric hyperspaces."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jos\u00e9 Manuel S\u00e1nchez \u00e1lvarez <\/strong><\/h2>\n<p>En los \u00faltimos a\u00f1os se ha desarrollado una teor\u00eda matem\u00e1tica que permite generalizar algunas teor\u00edas matem\u00e1ticas cl\u00e1sicas: hiperespacios, espacios de funciones, topolog\u00eda algebraica, etc. Este hecho viene motivado, en parte, por ciertos problemas de an\u00e1lisis funcional, concentraci\u00f3n de medidas, sistemas din\u00e1micos, teor\u00eda de las ciencias de la computaci\u00f3n, matem\u00e1tica econ\u00f3mica, etc.  esta tesis doctoral est\u00e1 dedicada al estudio de algunas de estas generalizaciones desde un punto de vista no sim\u00e9trico. En la primera parte, estudiamos el conjunto de funciones semi-lipschitz; mostramos que este conjunto admite una estructura de cono normado. Estudiaremos diversos tipos de completitud (bicompletitud, right k-completitud, d-completitud, etc), y tambi\u00e9n analizaremos cuando la casi-distancia correspondiente es balanceada. Adem\u00e1s presentamos un modelo adecuado para el computo de la complejidad de ciertos algoritmos mediante el uso de normas relativas. Esto se consigue seleccionando un espacio de funciones semi-lipschitz apropiado. Por otra parte, mostraremos que estos espacios proporcionan un contexto adecuado en el que caracterizar los puntos de mejor aproximaci\u00f3n en espacios casi-m\u00e9tricos.  el hecho de que varias hipertopolog\u00edas hayan sido aplicadas con \u00e9xito en diversas \u00e1reas de ciencias de la computaci\u00f3n ha contribuido a un considerable aumento del inter\u00e9s en el estudio de los hiperespacios desde un punto de vista no sim\u00e9trico. As\u00ed, en la segunda parte de la tesis, estudiamos algunas condiciones de mejor aproximaci\u00f3n en el contexto de hiperespacios casi-m\u00e9tricos. Por otro lado, caracterizamos la completitud de un espacio uniforme usando la completitud de sieber-pervin, la de smyth y la d-completitud de su casi-uniformidad superior de hausdorff-bourbaki, definida en los subconjuntos compactos no vac\u00edos.   finalmente, introducimos dos nociones de hiperespacio casi-m\u00e9trico fuzzy que generalizan las correspondientes nociones de espacio m\u00e9trico fuzzy de kramosil y michalek, y<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Semi-lipschitz functions, best approximation, and fuzzy quasi-metric hyperspaces.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Semi-lipschitz functions, best approximation, and fuzzy quasi-metric hyperspaces. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jos\u00e9 Manuel S\u00e1nchez \u00e1lvarez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de Valencia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 16\/06\/2009<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Salvador Romaguera Bonilla<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: valent\u00edn Gregori gregori <\/li>\n<li>Francisco Javier Gutierrez Garc\u00eda (vocal)<\/li>\n<li>Miguel \u00e1ngel S\u00e1nchez granero (vocal)<\/li>\n<li>Manuel Sanchis lopez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jos\u00e9 Manuel S\u00e1nchez \u00e1lvarez En los \u00faltimos a\u00f1os se ha desarrollado una teor\u00eda matem\u00e1tica que permite generalizar [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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