{"id":1266,"date":"2017-09-25T11:45:24","date_gmt":"2017-09-25T09:45:24","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1266"},"modified":"2023-03-20T11:21:16","modified_gmt":"2023-03-20T10:21:16","slug":"isbells-density-theorem-and-intersection-of-sublocales","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1266","title":{"rendered":"Isbell&#8217;s density theorem and intersection of sublocales"},"content":{"rendered":"<p>When I wrote my <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=1224\">latest blog post<\/a>, there were many things I thought would be useful to know about sublocales.\u00a0 Those eventually turned out to be useless in that context.\u00a0 However, I think they should be known, in a more general context.\u00a0 In particular, I would like to stress Isbell&#8217;s amazing density theorem, an easy but rather counterintuitive result in locale theory, and its consequence on intersections of sublocales.\u00a0 Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=1251\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When I wrote my latest blog post, there were many things I thought would be useful to know about sublocales.\u00a0 Those eventually turned out to be useless in that context.\u00a0 However, I think they should be known, in a more &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1266\">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-1266","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\/1266","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=1266"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1266\/revisions"}],"predecessor-version":[{"id":1269,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1266\/revisions\/1269"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}