{"id":2252,"date":"2020-02-20T15:46:27","date_gmt":"2020-02-20T14:46:27","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2252"},"modified":"2023-03-20T11:36:10","modified_gmt":"2023-03-20T10:36:10","slug":"dcpos-built-as-graphs-of-functions","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2252","title":{"rendered":"Dcpos built as graphs of functions"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Let <em>X<\/em> and <em>P<\/em> be two dcpos, and let \u03c8 be a map from <em>X<\/em> to <em>P<\/em>.  When is the graph of \u03c8 a dcpo?  I will give you a funny sufficient condition, which involves the so-called d-topology, and Hausdorffness.  I will briefly explain how this can be used to show that every <strong>\u03a0<\/strong><sup>0<\/sup><sub>2<\/sub> subset of a continuous dcpo is domain-complete, namely, is homeomorphic to a G<sub>\u03b4<\/sub> subset of some other continuous dcpo.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=2226\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let X and P be two dcpos, and let \u03c8 be a map from X to P. When is the graph of \u03c8 a dcpo? I will give you a funny sufficient condition, which involves the so-called d-topology, and Hausdorffness. &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2252\">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":[60,59,61,56],"class_list":["post-2252","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-d-topology","tag-dcpo","tag-domain-complete","tag-quasi-polish-space"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2252","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=2252"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2252\/revisions"}],"predecessor-version":[{"id":2732,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2252\/revisions\/2732"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}