{"id":2912,"date":"2020-10-19T15:35:51","date_gmt":"2020-10-19T13:35:51","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2912"},"modified":"2023-03-20T11:31:09","modified_gmt":"2023-03-20T10:31:09","slug":"quasi-uniform-spaces-i-pervin-quasi-uniformities-pervin-spaces","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2912","title":{"rendered":"Quasi-Uniform Spaces I: Pervin Quasi-Uniformities, Pervin Spaces"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A <em>uniform space<\/em> is a natural generalization of the notion of a metric space, on which completeness still makes sense.  It is rather puzzling that I managed to avoid the subject of quasi-uniform spaces in something like the 7 years that this blog existed&#8230; and it is time that I started.  I will only say very classical things, and I will concentrate one a construction due to William Pervin, simplifying an earlier result of Cs\u00e1sz\u00e1r, and which shows that <em>every<\/em> topological space is quasi-uniformizable.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=2869\" data-type=\"page\" data-id=\"2869\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A uniform space is a natural generalization of the notion of a metric space, on which completeness still makes sense. It is rather puzzling that I managed to avoid the subject of quasi-uniform spaces in something like the 7 years &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2912\">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":[48],"class_list":["post-2912","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-quasi-uniform-space"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2912","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=2912"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2912\/revisions"}],"predecessor-version":[{"id":2913,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2912\/revisions\/2913"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2912"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2912"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}