{"id":903,"date":"2016-04-10T12:15:57","date_gmt":"2016-04-10T10:15:57","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=903"},"modified":"2023-03-20T11:21:40","modified_gmt":"2023-03-20T10:21:40","slug":"locales-sublocales-i","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=903","title":{"rendered":"Locales, sublocales I"},"content":{"rendered":"<p>Stone duality leads naturally to the idea of <em>locale<\/em> theory.\u00a0 Quickly said, the idea is that, instead of reasoning with topological spaces, we reason with frames.\u00a0 The two concepts are not completely interchangeable, but the <strong>O<\/strong> \u22a3 pt adjunction shows that they are close.\u00a0 My purpose today is to give an introduction to what the analogue of a topological\u00a0<em>subspace<\/em> should be on the localic side.\u00a0 Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=888\">full post<\/a>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Stone duality leads naturally to the idea of locale theory.\u00a0 Quickly said, the idea is that, instead of reasoning with topological spaces, we reason with frames.\u00a0 The two concepts are not completely interchangeable, but the O \u22a3 pt adjunction shows &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=903\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","footnotes":""},"categories":[1],"tags":[41,42],"class_list":["post-903","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-frame","tag-locale"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/903","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=903"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/903\/revisions"}],"predecessor-version":[{"id":904,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/903\/revisions\/904"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}