{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T10:33:50Z","timestamp":1725532430736},"reference-count":0,"publisher":"EasyChair","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>A poset model of  a  topological space X is a poset  P such that the subspace Max(P) of the Scott space \u03a3P consisting of all maximal points of P  is homeomorphic to X. Every T&amp;lt;sub&amp;gt;1&amp;lt;\/sub&amp;gt; space has a (bounded complete algebraic) poset model. It is, however,  not known whether every T&amp;lt;sub&amp;gt;1&amp;lt;\/sub&amp;gt;  space has a dcpo model and whether every sober T&amp;lt;sub&amp;gt;1&amp;lt;\/sub&amp;gt;  space has a dcpo model whose Scott topology is sober. In this paper we give a positive answer to these two problems. For each T&amp;lt;sub&amp;gt;1&amp;lt;\/sub&amp;gt;  space X we shall construct a dcpo A that is a model of X, and prove that X is sober if and only if the Scott topology of A is sober.  One useful by-product is a method that can be used to construct more non-sober dcpos.<\/jats:p>","DOI":"10.29007\/prcv","type":"proceedings-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T17:59:06Z","timestamp":1516730346000},"page":"221-216","source":"Crossref","is-referenced-by-count":0,"title":["Dcpo models of  T&lt;sub&gt;1&lt;\/sub&gt;   spaces"],"prefix":"10.29007","volume":"25","author":[{"given":"Zhao","family":"Dongsheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Xiaoyong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"11545","event":{"name":"TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic"},"container-title":["EPiC Series in Computing"],"original-title":[],"deposited":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T18:01:11Z","timestamp":1516730471000},"score":1,"resource":{"primary":{"URL":"https:\/\/easychair.org\/publications\/paper\/2J1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.29007\/prcv","relation":{},"ISSN":["2398-7340"],"issn-type":[{"type":"print","value":"2398-7340"}],"subject":[]}}