{"id":2985,"date":"2020-11-21T11:32:00","date_gmt":"2020-11-21T10:32:00","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2985"},"modified":"2023-03-20T11:30:57","modified_gmt":"2023-03-20T10:30:57","slug":"quasi-uniform-spaces-ii-stably-compact-spaces","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2985","title":{"rendered":"Quasi-uniform spaces II: Stably compact spaces"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">There is a standard result in the theory of uniform spaces that shows (again) how magical compact Hausdorff space can be: for every compact Hausdorff space <em>X<\/em>, there is a unique uniformity that induces the topology of <em>X<\/em>, and its entourages are exactly the neighborhoods of the diagonal.  How can we generalize this to stably compact spaces?  No, the topology of a stably compact space is not induced by a unique quasi-uniformity&#8230; the result has to be a bit more subtle than that.  In passing, we will see that every core-compact space, and in particular every locally compact space, has a minimal compatible quasi-uniformity, which has a very simple description.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=2915\" data-type=\"page\" data-id=\"2915\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There is a standard result in the theory of uniform spaces that shows (again) how magical compact Hausdorff space can be: for every compact Hausdorff space X, there is a unique uniformity that induces the topology of X, and its &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2985\">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":[48,45],"class_list":["post-2985","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-quasi-uniform-space","tag-stably-compact-space"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2985","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=2985"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2985\/revisions"}],"predecessor-version":[{"id":2986,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2985\/revisions\/2986"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2985"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2985"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2985"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}