{"id":4060,"date":"2021-07-25T00:12:27","date_gmt":"2021-07-24T22:12:27","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4060"},"modified":"2023-03-20T11:25:53","modified_gmt":"2023-03-20T10:25:53","slug":"prestreams-and-d-spaces","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4060","title":{"rendered":"Prestreams and d-spaces"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">How do you model a topological space with a direction of time?  That should seem easy; for example, a topological space with a preordering should be enough.  But how do you model the directed circle, where times goes counterclockwise?  That should seem harder.  Fortunately, there are at least two satisfactory models: Marco Grandis&#8217; d-spaces, and Sanjeevi Krishnan&#8217;s (pre)streams, which I will describe.  Both appeared in 2009.  Although they look rather different, they are connected by an idempotent adjunction, which restricts to an equivalence between so-called complete d-spaces and Haucourt streams, as discovered by Emmanuel Haucourt in 2012.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=3981\" data-type=\"page\" data-id=\"3981\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How do you model a topological space with a direction of time? That should seem easy; for example, a topological space with a preordering should be enough. But how do you model the directed circle, where times goes counterclockwise? That &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4060\">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":[40,35],"class_list":["post-4060","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-d-space","tag-stream"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4060","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=4060"}],"version-history":[{"count":3,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4060\/revisions"}],"predecessor-version":[{"id":4064,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4060\/revisions\/4064"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}