{"id":1975,"date":"2019-07-20T09:31:21","date_gmt":"2019-07-20T07:31:21","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1975"},"modified":"2023-03-20T11:42:10","modified_gmt":"2023-03-20T10:42:10","slug":"bc-hulls-and-clat-hulls","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1975","title":{"rendered":"Bc-hulls and Clat-hulls"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Bounded-complete domains (bc-domains) are an incredibly useful form of continuous dcpos.  Given a continuous dcpo <em>X<\/em>, is there a completion of <em>X<\/em> as a bc-domain, for example a free bc-domain on <em>X<\/em>?  That does not exist in general, but Yuri Ershov showed that one can build a so-called <em>bc-hull<\/em> of any continuous dcpo in 1997.  I will describe what that is in the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=1899\">full post<\/a>.  My point is really to show that, despite the fact that it is a complicated construction in general, this really becomes a very simple, and familiar, one when <em>X<\/em> is <em>coherent<\/em>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bounded-complete domains (bc-domains) are an incredibly useful form of continuous dcpos. Given a continuous dcpo X, is there a completion of X as a bc-domain, for example a free bc-domain on X? That does not exist in general, but Yuri &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1975\">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":[68,69],"class_list":["post-1975","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-bounded-complete-dcpo","tag-complete-lattice"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1975","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=1975"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1975\/revisions"}],"predecessor-version":[{"id":1976,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1975\/revisions\/1976"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}