{"id":979,"date":"2016-08-25T11:57:13","date_gmt":"2016-08-25T09:57:13","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=979"},"modified":"2022-11-19T15:23:45","modified_gmt":"2022-11-19T14:23:45","slug":"the-dolecki-greco-lechicki-theorem","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=979","title":{"rendered":"The Dolecki-Greco-Lechicki Theorem"},"content":{"rendered":"<p>I have met <a href=\"https:\/\/dolecki.perso.math.cnrs.fr\/\">Szymon Dolecki<\/a> at the <a href=\"https:\/\/www2.le.ac.uk\/conference\/topology2016\">Summer Topology Conference 2016<\/a>, and he is a charming person.\u00a0 In 1995, with Gabriele Greco and Alojzy Lechicki, he proved a very nice theorem \u2014 every \u010cech-complete space is consonant \u2014 that deserves to be well-known.\u00a0 As a coincidence, this very theorem was mentioned by <a href=\"https:\/\/www.math.lsu.edu\/~lawson\/\">Jimmie Lawson<\/a> at the same conference.\u00a0 It is also the subject of Exercise 8.3.4 in the <a href=\"https:\/\/www.cambridge.org\/gb\/knowledge\/isbn\/item7069109\/Non-Hausdorff%20Topology%20and%20Domain%20Theory\/?site_locale=en_GB\">book<\/a>, but I am afraid that, as stated, it is way too hard. My purpose here is to give a complete solution to the exercise.\u00a0 The proof is elementary, that is, it does not require any deep knowledge of topology.\u00a0 Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=964\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have met Szymon Dolecki at the Summer Topology Conference 2016, and he is a charming person.\u00a0 In 1995, with Gabriele Greco and Alojzy Lechicki, he proved a very nice theorem \u2014 every \u010cech-complete space is consonant \u2014 that deserves &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=979\">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-979","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\/979","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=979"}],"version-history":[{"count":4,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/979\/revisions"}],"predecessor-version":[{"id":5946,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/979\/revisions\/5946"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}