{"id":2492,"date":"2020-05-20T10:36:10","date_gmt":"2020-05-20T08:36:10","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2492"},"modified":"2023-03-20T11:33:45","modified_gmt":"2023-03-20T10:33:45","slug":"quasi-polish-spaces-as-rounded-ideal-completions","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2492","title":{"rendered":"Quasi-Polish spaces as rounded ideal completions"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">This month, a pearl by Matthew de Brecht.  It is known that the rounded ideal completion of an abstract basis (a set <em>B<\/em> with a transitive, interpolative relation) is a continuous dcpo, and that all continuous dcpos can be obtained this way.  What do you get if you remove the requirement of interpolation?  Well, and assuming <em>B<\/em> countable&#8230; exactly the quasi-Polish spaces!  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=2416\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This month, a pearl by Matthew de Brecht. It is known that the rounded ideal completion of an abstract basis (a set B with a transitive, interpolative relation) is a continuous dcpo, and that all continuous dcpos can be obtained &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2492\">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":[57,56],"class_list":["post-2492","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-completion","tag-quasi-polish-space"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2492","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=2492"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2492\/revisions"}],"predecessor-version":[{"id":2494,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2492\/revisions\/2494"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2492"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}