{"id":3364,"date":"2021-02-22T15:32:22","date_gmt":"2021-02-22T14:32:22","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=3364"},"modified":"2023-03-20T11:30:05","modified_gmt":"2023-03-20T10:30:05","slug":"quasi-continuous-domains-and-the-smyth-powerdomain","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=3364","title":{"rendered":"Quasi-continuous domains and the Smyth powerdomain"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">&#8220;Quasi-continuous domains and the Smyth powerdomain&#8221; is the title of a very nice 2013 paper by Reinhold Heckmann and Klaus Keimel.  I will <em>not<\/em> talk about quasi-continuous domains in this post.  Rather, I will mention three pearls that this paper contains: one on so-called supercompact sets, a second one now called the <em>topological Rudin Lemma<\/em>, and finally a pretty surprising characterization of sober spaces that looks a lot like the definition of well-filteredness.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=3258\" data-type=\"page\" data-id=\"3258\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;Quasi-continuous domains and the Smyth powerdomain&#8221; is the title of a very nice 2013 paper by Reinhold Heckmann and Klaus Keimel. I will not talk about quasi-continuous domains in this post. Rather, I will mention three pearls that this paper &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=3364\">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":{"footnotes":""},"categories":[1],"tags":[16,47],"class_list":["post-3364","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-powerdomain","tag-quasi-continuous-domain"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/3364","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=3364"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/3364\/revisions"}],"predecessor-version":[{"id":3365,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/3364\/revisions\/3365"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}