{"id":2839,"date":"2020-09-20T19:56:24","date_gmt":"2020-09-20T17:56:24","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2839"},"modified":"2023-03-20T11:31:27","modified_gmt":"2023-03-20T10:31:27","slug":"on-the-word-topology-and-beyond","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2839","title":{"rendered":"On the word topology, and beyond"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Today I (Jean G.-L.) have the pleasure to have a guest, <a href=\"https:\/\/www.lsv.ens-paris-saclay.fr\/~lopez\/\">Aliaume Lopez<\/a>.  We are going to talk about the word topology on <em>X<\/em>*.  In the <a href=\"https:\/\/www.cambridge.org\/gb\/knowledge\/isbn\/item7069109\/Non-Hausdorff%20Topology%20and%20Domain%20Theory\/?site_locale=en_GB\">book<\/a>, there is a so-called Topological Higman Lemma that says that, if <em>X<\/em> is a Noetherian space, then <em>X<\/em>* is Noetherian in the word topology, generalizing a famous theorem due to Graham Higman.  However, there used to be no characterization of the word topology as a universal construction, say as a finest topology or a coarsest topology with some properties.  Aliaume has managed to find a satisfactory, and simple, answer to this question.  We will then discuss the case of infinite words, and we will end with a conjecture which, if true, would provide us with a large set of new Noetherian spaces.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=2735\" data-type=\"page\" data-id=\"2735\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Today I (Jean G.-L.) have the pleasure to have a guest, Aliaume Lopez. We are going to talk about the word topology on X*. In the book, there is a so-called Topological Higman Lemma that says that, if X is &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2839\">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":[13,37],"class_list":["post-2839","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-noetherian","tag-wqo"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2839","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=2839"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2839\/revisions"}],"predecessor-version":[{"id":5896,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2839\/revisions\/5896"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2839"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2839"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}