{"id":1512,"date":"2018-06-21T18:58:51","date_gmt":"2018-06-21T16:58:51","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1512"},"modified":"2020-04-03T10:39:15","modified_gmt":"2020-04-03T08:39:15","slug":"dcpos-and-convergence-spaces-ii-preserving-products","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1512","title":{"rendered":"Dcpos and convergence spaces II: preserving products"},"content":{"rendered":"<p>Let us continue last month&#8217;s story. \u00a0We had define various structures of convergence spaces on a dcpo, which were all admissible in the sense that their topological modification is the Scott topology. \u00a0We shall see that equipping dcpos with their Heckmann, or with their Scott convergence structures, defines a product-preserving functor from\u00a0<strong>Dcpo<\/strong> to\u00a0<strong>Conv<\/strong>. \u00a0The result is due to Reinhold Heckmann, and contrasts with the fact that the similar functor from\u00a0<strong>Dcpo<\/strong> to\u00a0<strong>Top<\/strong> does\u00a0<em>not<\/em> preserve products\u2014a very nasty source of mistakes. \u00a0Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=1503\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let us continue last month&#8217;s story. \u00a0We had define various structures of convergence spaces on a dcpo, which were all admissible in the sense that their topological modification is the Scott topology. \u00a0We shall see that equipping dcpos with their &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1512\">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-1512","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\/1512","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=1512"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1512\/revisions"}],"predecessor-version":[{"id":1513,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1512\/revisions\/1513"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1512"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1512"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1512"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}