{"id":4792,"date":"2022-02-21T17:25:10","date_gmt":"2022-02-21T16:25:10","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4792"},"modified":"2023-02-20T19:26:43","modified_gmt":"2023-02-20T18:26:43","slug":"l-domains-stable-open-sets-and-stable-stone-duality","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4792","title":{"rendered":"L-domains, stable open sets, and stable Stone duality"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Stone duality relates topological spaces and locales (or frames).  But there are really many sorts of Stone dualities.  In 1997, Yixiang Chen studied Stone dualities that relate so-called L-domains to so-called distributive D-semilattices.  This was refined later in a common paper with Achim Jung.  This is a very nice theory, which looks a lot like ordinary Stone duality between topological spaces and frames, but with a few twists.  As we will see, the resulting monad, which I would like to call <em>algebraicization<\/em>, turns every L-domain into an algebraic L-domain.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=4689\" data-type=\"page\" data-id=\"4689\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Stone duality relates topological spaces and locales (or frames). But there are really many sorts of Stone dualities. In 1997, Yixiang Chen studied Stone dualities that relate so-called L-domains to so-called distributive D-semilattices. This was refined later in a common &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4792\">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":[32,33],"class_list":["post-4792","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-l-domain","tag-stone-duality"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4792","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=4792"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4792\/revisions"}],"predecessor-version":[{"id":4793,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4792\/revisions\/4793"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4792"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4792"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4792"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}