{"id":7526,"date":"2023-11-20T16:03:08","date_gmt":"2023-11-20T15:03:08","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=7526"},"modified":"2023-11-20T16:25:50","modified_gmt":"2023-11-20T15:25:50","slug":"compact-semilattices-without-small-semilattices-ii-gierzs-counterexample","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=7526","title":{"rendered":"Compact semilattices without small semilattices II: Gierz&#8217;s counterexample"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">We pursue last month&#8217;s post, written with <a href=\"https:\/\/www.researchgate.net\/profile\/Zhenchao-Lyu\">Zhenchao Lyu<\/a>, and we describe Gierz&#8217;s example of a compact semilattice \u2014 namely, a compact Hausdorff topological semilattice \u2014 which does not have small semilattices.  It is a bit simpler than <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=4939\">Jimmie Lawson&#8217;s counterexample<\/a>, which was already described on this blog.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=7462\" data-type=\"page\" data-id=\"7462\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We pursue last month&#8217;s post, written with Zhenchao Lyu, and we describe Gierz&#8217;s example of a compact semilattice \u2014 namely, a compact Hausdorff topological semilattice \u2014 which does not have small semilattices. It is a bit simpler than Jimmie Lawson&#8217;s &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=7526\">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-7526","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\/7526","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=7526"}],"version-history":[{"count":3,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/7526\/revisions"}],"predecessor-version":[{"id":7531,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/7526\/revisions\/7531"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7526"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7526"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7526"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}