{"id":5994,"date":"2022-11-20T09:00:57","date_gmt":"2022-11-20T08:00:57","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5994"},"modified":"2023-02-20T19:18:38","modified_gmt":"2023-02-20T18:18:38","slug":"weakly-hausdorff-spaces-and-locally-strongly-sober-spaces","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5994","title":{"rendered":"Weakly Hausdorff spaces, and locally strongly sober spaces"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A funny convergence of topics happened a few weeks ago.  Fr\u00e9d\u00e9ric Mynard told me about so-called locally strongly sober spaces (which, I am ashamed to say, I had heard about but completely forgotten about).  At the same time, I was interested in so-called weakly Hausdorff spaces, as defined by Klaus Keimel and Jimmie Lawson in their paper on measure extension theorems for T<sub>0<\/sub> spaces.  I realized that those two classes of spaces had a lot in common, and this led me to inquire whether that was a coincidence.  As you may guess, this is not: we will see that the locally strongly sober spaces are exactly the weakly Hausdorff, coherent sober spaces.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=5729\" data-type=\"page\" data-id=\"5729\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A funny convergence of topics happened a few weeks ago. Fr\u00e9d\u00e9ric Mynard told me about so-called locally strongly sober spaces (which, I am ashamed to say, I had heard about but completely forgotten about). At the same time, I was &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5994\">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":[14],"class_list":["post-5994","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-filters"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5994","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=5994"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5994\/revisions"}],"predecessor-version":[{"id":5996,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5994\/revisions\/5996"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5994"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5994"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5994"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}