{"id":929,"date":"2016-05-11T19:04:18","date_gmt":"2016-05-11T17:04:18","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=929"},"modified":"2023-03-20T11:21:33","modified_gmt":"2023-03-20T10:21:33","slug":"locales-sublocales-ii-sieves","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=929","title":{"rendered":"Locales, sublocales II: sieves"},"content":{"rendered":"<p>Last time, I promised you we would explore another way of defining sublocales.\u00a0 We shall again use the naive approach that consists in imagining how we would encode subspaces of a T<sub>0<\/sub> topological space <em>X<\/em> by looking at open subsets only, and certainly not at points.\u00a0 We shall encode a localic version of the notion of subspaces through what I call <em>sieves<\/em>, which are certain sets of <em>formal crescents<\/em>.\u00a0 I&#8217;ll then show you that this gives you a complete lattice that is isomorphic to the lattice of sublocales that we have seen last time.\u00a0 See the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=908\">full post<\/a>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Last time, I promised you we would explore another way of defining sublocales.\u00a0 We shall again use the naive approach that consists in imagining how we would encode subspaces of a T0 topological space X by looking at open subsets &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=929\">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":[41,42],"class_list":["post-929","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-frame","tag-locale"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/929","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=929"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/929\/revisions"}],"predecessor-version":[{"id":930,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/929\/revisions\/930"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=929"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=929"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}