{"id":7068,"date":"2023-07-20T08:01:00","date_gmt":"2023-07-20T06:01:00","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=7068"},"modified":"2023-07-14T11:32:57","modified_gmt":"2023-07-14T09:32:57","slug":"exponentiable-locales-ii-the-exponentiable-locales-are-the-continuous-frames","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=7068","title":{"rendered":"Exponentiable locales II: the exponentiable locales are the continuous frames"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=6714\" data-type=\"page\" data-id=\"6714\">Two months ago<\/a>, we have seen that every exponentiable locale had to be continuous, as a frame.  We will see that the converse holds: the continuous frames are exactly the exponentiable locales.  The result is due to Martin Hyland in 1979.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=6841\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Two months ago, we have seen that every exponentiable locale had to be continuous, as a frame. We will see that the converse holds: the continuous frames are exactly the exponentiable locales. The result is due to Martin Hyland in &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=7068\">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":[21,72,42],"class_list":["post-7068","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-continuous-lattice","tag-exponentiability","tag-locale"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/7068","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=7068"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/7068\/revisions"}],"predecessor-version":[{"id":7074,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/7068\/revisions\/7074"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7068"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7068"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7068"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}