{"id":1415,"date":"2018-02-26T14:19:16","date_gmt":"2018-02-26T13:19:16","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1415"},"modified":"2018-04-29T18:23:12","modified_gmt":"2018-04-29T16:23:12","slug":"meet-continuous-spaces","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1415","title":{"rendered":"Meet-continuous spaces"},"content":{"rendered":"<p>Meet-continuous dcpos were defined and studied by\u00a0<span class=\"authors__name\">Hui\u00a0Kou,\u00a0<\/span>Ying-Ming\u00a0Liu, and Mao-Kang\u00a0Luo about 14 years ago, and their importance only starts to be appreciated now. \u00a0One of the leading results in the theory of meet-continuous dcpos is that a dcpo is continuous if and only if it is quasi-continuous and meet-continuous. \u00a0Weng Kin Ho, Achim Jung and Dongsheng Zhao&#8217;s gave a <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=737\">new proof<\/a> of that theorem through Stone duality. \u00a0Today, I would like to talk about yet another proof, which I had the pleasure to read in\u00a0<a href=\"https:\/\/www.cs.bham.ac.uk\/people\/Xiaodong%20Jia\">Xiaodong Jia<\/a>&#8216;s remarkable PhD thesis. Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=1396\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Meet-continuous dcpos were defined and studied by\u00a0Hui\u00a0Kou,\u00a0Ying-Ming\u00a0Liu, and Mao-Kang\u00a0Luo about 14 years ago, and their importance only starts to be appreciated now. \u00a0One of the leading results in the theory of meet-continuous dcpos is that a dcpo is continuous if &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1415\">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-1415","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\/1415","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=1415"}],"version-history":[{"count":3,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1415\/revisions"}],"predecessor-version":[{"id":1426,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1415\/revisions\/1426"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1415"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1415"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1415"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}