{"id":610,"date":"2015-03-25T15:42:35","date_gmt":"2015-03-25T14:42:35","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=610"},"modified":"2017-10-30T17:09:44","modified_gmt":"2017-10-30T16:09:44","slug":"610","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=610","title":{"rendered":"Hyperspaces and powerdomains I: closed and open sets"},"content":{"rendered":"<p>While a topological space is a space of points, a hyperspace is a space of subsets, with a suitable topology.\u00a0 Examples abound in the literature.\u00a0 For example, the so-called Smyth powerdomain (Proposition 8.3.25) is one.\u00a0 To start the series, let me look at the Hoare hyperspace instead.\u00a0 We shall see that it is a space that has many nice properties.\u00a0 I won&#8217;t say to which purpose it has been put in denotational semantics yet, or that it defines a monad with a very natural inequational theory&#8230; all that will have to wait!\u00a0 Read the <a title=\"Powerdomains and hyperspaces I: closed and open subsets\" href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=585\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>While a topological space is a space of points, a hyperspace is a space of subsets, with a suitable topology.\u00a0 Examples abound in the literature.\u00a0 For example, the so-called Smyth powerdomain (Proposition 8.3.25) is one.\u00a0 To start the series, let &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=610\">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-610","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\/610","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=610"}],"version-history":[{"count":3,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/610\/revisions"}],"predecessor-version":[{"id":1293,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/610\/revisions\/1293"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=610"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=610"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=610"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}