{"id":330,"date":"2014-01-21T16:53:15","date_gmt":"2014-01-21T15:53:15","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=330"},"modified":"2017-10-30T17:10:25","modified_gmt":"2017-10-30T16:10:25","slug":"filters-part-iii-pseudo-topologies","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=330","title":{"rendered":"Filters, part III: pretopologies"},"content":{"rendered":"<p>While listening to some talks at the special session on categorical topology last Saturday, I realized that I had said something wrong at the end of <a title=\"Filters, part II: filter spaces\" href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=283\">part II<\/a>: the filter spaces satisfying the property that any intersection of filters that converge to a point <em>x<\/em> must also converge to <em>x<\/em> are not the topological filter spaces, but the <em>pre<\/em>topological filter spaces.\u00a0 See the <a title=\"Filters, part III\" href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=319\">full post<\/a> for an in-depth discussion of the matter.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>While listening to some talks at the special session on categorical topology last Saturday, I realized that I had said something wrong at the end of part II: the filter spaces satisfying the property that any intersection of filters that &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=330\">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-330","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\/330","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=330"}],"version-history":[{"count":6,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/330\/revisions"}],"predecessor-version":[{"id":1299,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/330\/revisions\/1299"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}