{"id":868,"date":"2016-01-27T14:33:12","date_gmt":"2016-01-27T13:33:12","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=868"},"modified":"2017-10-30T17:08:58","modified_gmt":"2017-10-30T16:08:58","slug":"remainders-bqos-and-quasi-polish-spaces-again","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=868","title":{"rendered":"Remainders, bqos, and quasi-Polish spaces again"},"content":{"rendered":"<p>In my first post on <a title=\"Ideal models I\" 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&#8217;s result from metric to quasi-metric spaces. That was more complicated than what I had thought.<\/p>\n<p>Along my journey, I (re)discovered a few results, some old, some new, on ideal completion remainders\u2014namely, the spaces you get by taking the ideal completion of a poset\u00a0<em>P<\/em>, and substracting <em>P<\/em> off\u2014and on the related notion of sobrification remainders.\u00a0 That may seem like silly notions to you, and I certainly thought so until recently.\u00a0 But they seem to crop up from time to time.<\/p>\n<p>I will show you that <em>every<\/em> T<sub>0<\/sub> space occurs as a sobrification remainder (a result due to R.-E. Hoffmann), and I will give you the rough idea of a proof that the ideal completion remainders of countable posets are exactly the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=47\">quasi-Polish spaces<\/a> (a result due to M. de Brecht). I will also describe an intriguing result on wqos and bqos due to Y. P\u00e9quignot and R. Carroy. Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=865\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In my first post on ideal domains, I thought I would be able to extend Keye Martin&#8217;s result from metric to quasi-metric spaces. That was more complicated than what I had thought. Along my journey, I (re)discovered a few results, &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=868\">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-868","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\/868","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=868"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/868\/revisions"}],"predecessor-version":[{"id":869,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/868\/revisions\/869"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=868"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=868"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=868"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}