{"id":1196,"date":"2017-04-28T23:10:50","date_gmt":"2017-04-28T21:10:50","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1196"},"modified":"2017-10-30T17:08:00","modified_gmt":"2017-10-30T16:08:00","slug":"bounded-complete-and-dcpo-models-of-t1-spaces","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1196","title":{"rendered":"Bounded complete and dcpo models of T1 spaces"},"content":{"rendered":"<p>The nice thing about colleagues is that, sometimes, they give me a primer on their latest results.\u00a0 I would like to talk about a strange result by Dongsheng Zhao and Xiaoyong Xi, which, while accepted for publication, does not seem to be out yet.\u00a0 (Thanks to D. Zhao for letting me know about this!)\u00a0 I have already talked about models of topological spaces.\u00a0 Following earlier results by Zhao, Xi, and Ern\u00e9, one can show that every T<sub>1<\/sub> space has a bounded complete, and even algebraic, <em>poset<\/em> model, and that every T<sub>1<\/sub> space has a (not bounded complete) <em>dcpo<\/em> model, but can we have both at the same time?\u00a0 In other words, does every T<sub>1<\/sub> space have a bounded complete dcpo model?\u00a0 Answer (and explanations) in the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=1184\">full post&#8230;<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The nice thing about colleagues is that, sometimes, they give me a primer on their latest results.\u00a0 I would like to talk about a strange result by Dongsheng Zhao and Xiaoyong Xi, which, while accepted for publication, does not seem &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1196\">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":[],"class_list":["post-1196","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1196","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=1196"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1196\/revisions"}],"predecessor-version":[{"id":1201,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1196\/revisions\/1201"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1196"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1196"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}