{"id":528,"date":"2014-11-30T17:48:23","date_gmt":"2014-11-30T16:48:23","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=528"},"modified":"2017-10-30T17:10:05","modified_gmt":"2017-10-30T16:10:05","slug":"quasi-continuous-dcpos-and-locally-finitary-compact-spaces","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=528","title":{"rendered":"Quasi-continuous dcpos and locally finitary compact spaces"},"content":{"rendered":"<p>Although I am trying to post about every month, I have not posted anything for two months.\u00a0 My first idea was to talk about synthetic topology, after I read some papers by <a title=\"Weng Kin Ho\" href=\"https:\/\/math.nie.edu.sg\/people\/acad\/staffdetail\/HoWengKin.html\">Weng Kin Ho<\/a> and by <a title=\"Martin Escardo\" href=\"https:\/\/www.cs.bham.ac.uk\/~mhe\/\">Mart\u00edn H\u00f6tzel Escard\u00f3<\/a>. \u00a0 I soon realized I would have trouble to match the level of clarity they reach in their papers.\u00a0 Let me recommend [1], or [2] if you&#8217;ve got more time.\u00a0 Maybe I&#8217;ll talk about these one day, who knows.<\/p>\n<p>In the meantime, I realized I&#8217;ve never talked about any of my research.\u00a0 Last year, Achim Jung and myself found a nifty theorem, one of those theorems in mathematics that states that several, apparently unrelated notions are in fact the same.\u00a0 Jimmie Lawson and Xiaoyong Xi found the same result independently.\u00a0 This all builds on the related notions of locally finitary compact spaces, and of quasi-continuous dcpos, and I&#8217;ll start to introduce you to the latter.\u00a0 See the <a title=\"Quasi-continuous dcpos and locally finitary compact spaces\" href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=521\">full post<\/a>.<\/p>\n<p>&nbsp;<\/p>\n<p>[1]\u00a0Mart\u00edn H\u00f6tzel Escard\u00f3 and Weng Kin Ho. <a href=\"https:\/\/math.nie.edu.sg\/wkho\/Research%5CMy%20publications%5CCS%20applications%5CYINCO3616-published.pdf\"><em>An operational domain theory and topology of a sequential programming language.<\/em><\/a> Information and Computation 207(3), p. 411-437, Elsevier, 2009.<\/p>\n<p>[2] Mart\u00edn H\u00f6tzel Escard\u00f3. <a title=\"Synthetic topology\" href=\"https:\/\/www.cs.bham.ac.uk\/~mhe\/papers\/entcs87.pdf\">Synthetic topology of data types and classical spaces<\/a>. ENTCS, Elsevier, volume 87, pages 21-156, November 2004.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Although I am trying to post about every month, I have not posted anything for two months.\u00a0 My first idea was to talk about synthetic topology, after I read some papers by Weng Kin Ho and by Mart\u00edn H\u00f6tzel Escard\u00f3. &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=528\">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":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-528","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\/528","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=528"}],"version-history":[{"count":3,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/528\/revisions"}],"predecessor-version":[{"id":1296,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/528\/revisions\/1296"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=528"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=528"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}