{"id":842,"date":"2016-01-03T15:56:04","date_gmt":"2016-01-03T14:56:04","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=842"},"modified":"2017-10-30T17:09:02","modified_gmt":"2017-10-30T16:09:02","slug":"ideal-models-ii","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=842","title":{"rendered":"Ideal models II"},"content":{"rendered":"<p>Last time, we have seen that every completely metrizable space <em>X<\/em> has an ideal model, that is, that <em>X<\/em> can be embedded into an ideal domain <em>Y <\/em>in such a way that we can equate <em>X<\/em> with the subspace of maximal elements of Y.<\/p>\n<p>We have also seen the converse to that: if <em>X<\/em> is a metrizable space with an ideal model, then <em>X<\/em> is completely metrizable.<\/p>\n<p>But we had skipped an essential ingredient: that the set <em>X<\/em> of maximal elements of an ideal model <em>Y<\/em> is a G<sub>\u03b4<\/sub> subset of <em>Y<\/em>.\u00a0 This is true, but complicated.\u00a0 As I have already said last time, we shall do something slightly simpler.\u00a0 See the <a title=\"Ideal models II\" href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=808\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Last time, we have seen that every completely metrizable space X has an ideal model, that is, that X can be embedded into an ideal domain Y in such a way that we can equate X with the subspace of &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=842\">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":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-842","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\/842","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=842"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/842\/revisions"}],"predecessor-version":[{"id":1286,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/842\/revisions\/1286"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}