{"id":1699,"date":"2024-12-12T23:53:37","date_gmt":"2024-12-12T23:53:37","guid":{"rendered":"https:\/\/blogschapman.wpenginepowered.com\/gci\/2024\/12\/12\/dr-ana-belen-avilez-garcia-what-is-point-free-topology\/"},"modified":"2026-07-20T06:02:42","modified_gmt":"2026-07-20T06:02:42","slug":"dr-ana-belen-avilez-garcia-what-is-point-free-topology","status":"publish","type":"post","link":"https:\/\/blogs.chapman.edu\/gci\/2024\/12\/12\/dr-ana-belen-avilez-garcia-what-is-point-free-topology\/","title":{"rendered":"Dr. Ana Bel\u00e9n Avilez Garc\u00eda: What is point"},"content":{"rendered":"

At our 2024 GCI Postdoc Showcase, Postdoctoral Fellow Ana Bel\u00e9n Avilez Garc\u00eda presented a poster about different perspectives with point-free topology. To learn more about her research, reach out to Dr. Avilez Garc\u00eda at avilezgarcia@chapman.edu.<\/p>\n

ABSTRACT: Point-free topology is regarded as an algebraic (more specifically, lattice theoretical) counterpart of classical topology. Locales and frames, the objects of study, are a generalized version of topological spaces where one focuses on their lattices of open sets, leaving aside the points. Replacing the category of topological spaces and continuous maps by the category of locales and their maps has allowed to approach topology from a different perspective, with advantages over the classical perspective.\u00a0<\/em><\/p>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

free topology?<\/p>\n","protected":false},"author":5302,"featured_media":1747,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"custom_author_name":"","chapman_pin_hero_slider":"","footnotes":""},"categories":[2],"tags":[],"class_list":["post-1699","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gci-fellows"],"yoast_head":"\nGrand Challenges Initiative | Chapman Blogs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.chapman.edu\/gci\/2024\/12\/12\/dr-ana-belen-avilez-garcia-what-is-point-free-topology\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Dr. Ana Bel\u00e9n Avilez Garc\u00eda: What is point - 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