{"id":882,"date":"2016-03-10T09:15:44","date_gmt":"2016-03-10T08:15:44","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=882"},"modified":"2017-10-30T17:08:53","modified_gmt":"2017-10-30T16:08:53","slug":"ideal-models-iii-quasi-ideal-domains","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=882","title":{"rendered":"Ideal Models III: Quasi-ideal domains"},"content":{"rendered":"<p>I am a bit stubborn. In my first post on <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=681\">ideal domains<\/a>, I thought I would be able to extend Keye Martin\u2019s result from metric to quasi-metric spaces. I have said I had failed, but now I think I have succeeded.\u00a0 This leads to a notion that I will call a <em>quasi-ideal domain<\/em>.<\/p>\n<p>Our purpose today is to show that, if <em>X<\/em> is a continuous Yoneda-complete quasi-metric space, then it embeds into an algebraic dcpo, and in fact, in a very specific way: as the subspace of limit elements of a quasi-ideal domain.\u00a0 Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=838\">full post<\/a>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I am a bit stubborn. In my first post on ideal domains, I thought I would be able to extend Keye Martin\u2019s result from metric to quasi-metric spaces. I have said I had failed, but now I think I have &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=882\">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-882","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\/882","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=882"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/882\/revisions"}],"predecessor-version":[{"id":883,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/882\/revisions\/883"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=882"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=882"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=882"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}