{"id":3127,"date":"2020-12-20T11:48:03","date_gmt":"2020-12-20T10:48:03","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=3127"},"modified":"2023-03-20T11:30:40","modified_gmt":"2023-03-20T10:30:40","slug":"quasi-uniform-spaces-iii-smyth-completeness-symcompactness","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=3127","title":{"rendered":"Quasi-uniform spaces III: Smyth-completeness, symcompactness"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">We embark on the study of notions of completeness for quasi-uniform spaces, and we concentrate on Smyth-completeness.  We will see that at least two familiar theorems from the realm of quasi-metric spaces generalize to quasi-uniform spaces: all Smyth-complete quasi-uniform spaces are quasi-sober, and the symcompact quasi-uniform spaces are exactly those that are Smyth-complete and totally bounded.  However, and especially for the latter result, the proofs will be trickier.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=2998\" data-type=\"page\" data-id=\"2998\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We embark on the study of notions of completeness for quasi-uniform spaces, and we concentrate on Smyth-completeness. We will see that at least two familiar theorems from the realm of quasi-metric spaces generalize to quasi-uniform spaces: all Smyth-complete quasi-uniform spaces &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=3127\">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":[50,48],"class_list":["post-3127","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-completeness","tag-quasi-uniform-space"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/3127","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=3127"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/3127\/revisions"}],"predecessor-version":[{"id":3128,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/3127\/revisions\/3128"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}