{"id":5496,"date":"2022-06-20T11:25:54","date_gmt":"2022-06-20T09:25:54","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5496"},"modified":"2023-02-20T19:23:50","modified_gmt":"2023-02-20T18:23:50","slug":"q-is-not-consonant-the-costantini-watson-argument","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5496","title":{"rendered":"Q is not consonant: the Costantini-Watson argument"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">I have already given an argument for the non-consonance of the Sorgenfrey line <strong>R<\/strong><sub>\u2113<\/sub> <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=3685\">here<\/a>.  I would now like to explain why the space <strong>Q<\/strong> of rational numbers is not consonant either.  That is quite a challenge.  The most easily accessible proof is due to Costantini and Watson, but it still requires some effort to understand.  Fortunately, the topological game of <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=4926\" data-type=\"page\" data-id=\"4926\">last time<\/a> will help us make sense of at least one half of the construction.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=5109\" data-type=\"page\" data-id=\"5109\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have already given an argument for the non-consonance of the Sorgenfrey line R\u2113 here. I would now like to explain why the space Q of rational numbers is not consonant either. That is quite a challenge. The most easily &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5496\">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":[25,11,18,10,26],"class_list":["post-5496","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-compact","tag-consonance","tag-counterexample","tag-game","tag-scattered"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5496","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=5496"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5496\/revisions"}],"predecessor-version":[{"id":5497,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5496\/revisions\/5497"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}