{"id":1842,"date":"2019-04-21T16:11:14","date_gmt":"2019-04-21T14:11:14","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1842"},"modified":"2020-04-03T10:38:14","modified_gmt":"2020-04-03T08:38:14","slug":"isbells-non-sober-complete-lattice","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1842","title":{"rendered":"Isbell&#8217;s non sober complete lattice"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Johnstone space <strong>J<\/strong> (1981) is the most famous example of a non-sober dcpo.  In 1982, Isbell came up with a non-sober <em>complete lattice<\/em>.  His construction is so complex that most authors use it as a black box.  I would like to explain how Isbell&#8217;s non-sober complete lattice is constructed.  As you can expect, this is a pretty clever construction, but I claim this is understandable.  I will conclude with remarkable results of Xu, Xi, and Zhao (2019), who proved that there even exists a non-sober <em>frame<\/em>.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=1785\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Johnstone space J (1981) is the most famous example of a non-sober dcpo. In 1982, Isbell came up with a non-sober complete lattice. His construction is so complex that most authors use it as a black box. I would like &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1842\">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-1842","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\/1842","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=1842"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1842\/revisions"}],"predecessor-version":[{"id":1843,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1842\/revisions\/1843"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}