{"id":65983,"date":"2008-05-07T00:00:00","date_gmt":"2008-05-07T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/topologa%c2%adas-localmente-quasi-convexas-en-grupos-topologicos-abelianos-weak-and-strong-topologies-in-topological-abelian-groups\/"},"modified":"2008-05-07T00:00:00","modified_gmt":"2008-05-07T00:00:00","slug":"topologa%c2%adas-localmente-quasi-convexas-en-grupos-topologicos-abelianos-weak-and-strong-topologies-in-topological-abelian-groups","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/topologa%c2%adas-localmente-quasi-convexas-en-grupos-topologicos-abelianos-weak-and-strong-topologies-in-topological-abelian-groups\/","title":{"rendered":"Topolog\u00edas localmente quasi- convexas en grupos topol\u00f3gicos abelianos.(weak and strong topologies in topological abelian groups)."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Lorenzo De Leo <\/strong><\/h2>\n<p>Null en el marco de los espacios vectoriales topol\u00f3gicos, nociones como topolog\u00eda d\u00e9bil, topolog\u00eda de mackey y topolog\u00eda fuerte son primordialmente el objeto de estudio de la teor\u00eda de dualidad. La extensi\u00f3n de la teor\u00eda de dualidad a la clase m\u00e1s amplia de los grupos topol\u00f3gicos abelianos encuentra serios obst\u00e1culos, como por ejemplo la falta de sentido de la noci\u00f3n de convexidad, que es  la piedra angular en dicha teor\u00eda. a lo largo de la presente memoria probamos resultados nuevos que permiten amp liar el conocimiento de las topolog\u00edas d\u00e9biles y fuertes en los grupos localmente cuasi-convexos. Para lograr nuestro objetivo, hemos consolidado el conocimiento de la topolog\u00eda de bohr y de la teor\u00eda de los subconjuntos cuasi-convex de un grupo topo l\u00f3gico.   la tesis est\u00e1 estructura en tres partes: 1) los conjuntos cuasi-convexos: sobre la estructura y caracterizaci\u00f3n de subconjuntos cuasi-convexos. Incluso en grupos elementales como los enteros o el c\u00edrculo unitario complejo no hay criterios d eterminantes para dilucidar si un subconjunto es o no cuasi-convexo. Hemos dado luz sobre estos conjuntos, y hemos descrito distintas aplicaciones de inter\u00e9s m\u00e1s general. 2) nuevos aspectos de la topolog\u00eda de bohr y otros tipos de topolog\u00edas \u00abd\u00e9biles \u00ab. 3) la topolog\u00eda de mackey de un grupo topol\u00f3gico abeliano. De hecho, esta definici\u00f3n aparece por primera vez en esta tesis. El estudio en profundidad de esta topolog\u00eda es la motivacci\u00f3n que subyace en las dem\u00e1s secciones de la memoria. Hemos avanz ado sobre lo que ya se sab\u00eda dando resultados nuevos y estructurando m\u00e1s de fondo la teor\u00eda.  inclu\u00edmos resultados obtenidos conjuntamente con d. Dikranjan y con m. Tkachenko, y recogidos en sendos  trabajos de pr\u00f3xima publicaci\u00f3n. M\u00e1s publicaciones con los resultados de la tesis est\u00e1n en proceso de preparaci\u00f3n.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Topolog\u00edas localmente quasi- convexas en grupos topol\u00f3gicos abelianos.(weak and strong topologies in topological abelian groups).<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Topolog\u00edas localmente quasi- convexas en grupos topol\u00f3gicos abelianos.(weak and strong topologies in topological abelian groups). <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Lorenzo De Leo <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Complutense de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 05\/07\/2008<\/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>Elena Mart\u00edn Peinador<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: lydia Aubenhofer <\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Lorenzo De Leo Null en el marco de los espacios vectoriales topol\u00f3gicos, nociones como topolog\u00eda d\u00e9bil, topolog\u00eda [&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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