{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:56Z","timestamp":1753889936949,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2018,5,16]],"date-time":"2018-05-16T00:00:00Z","timestamp":1526428800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,5,16]],"date-time":"2018-05-16T00:00:00Z","timestamp":1526428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,5,16]],"date-time":"2018-05-16T00:00:00Z","timestamp":1526428800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>In analogy to a result due to Drake and Thron about topological spaces, this paper studies the dcpos (directed complete posets) which are fully determined, among all dcpos, by their lattices of all Scott-closed subsets (such dcpos will be called $C_{\\sigma}$-unique).   We introduce the notions of down-linear element and quasicontinuous element in dcpos, and use them to prove that dcpos of certain classes, including all quasicontinuous dcpos as well as Johnstone's and Kou's examples, are $C_{\\sigma}$-unique. As a consequence, $C_{\\sigma}$-unique dcpos with their Scott topologies need not be bounded sober.<\/jats:p><jats:p>Comment: 12 pages. arXiv admin note: substantial text overlap with   arXiv:1607.03576<\/jats:p>","DOI":"10.23638\/lmcs-14(2:10)2018","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:27:58Z","timestamp":1743701278000},"source":"Crossref","is-referenced-by-count":0,"title":["Uniqueness of directed complete posets based on Scott closed set lattices"],"prefix":"10.23638","volume":"Volume 14, Issue 2","author":[{"given":"Dongsheng","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luoshan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2018,5,16]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1709.03700v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1709.03700v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:27:58Z","timestamp":1743701278000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/1530"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,16]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-14(2:10)2018","relation":{"has-preprint":[{"id-type":"arxiv","id":"1709.03700v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1709.03700v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1607.03576v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1709.03700","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1709.03700","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2018,5,16]]},"article-number":"1530"}}