{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T10:27:04Z","timestamp":1769077624014,"version":"3.49.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2018,4,27]],"date-time":"2018-04-27T00:00:00Z","timestamp":1524787200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,4,27]],"date-time":"2018-04-27T00:00:00Z","timestamp":1524787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,4,27]],"date-time":"2018-04-27T00:00:00Z","timestamp":1524787200000},"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 this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators offer a fresh perspective to existing concepts and results in domain theory, but also reveal ways to establishing novel domain-theoretic results. For instance, (1) the well-known interpolation property of the way-below relation on a continuous poset is equivalent to the idempotence of a certain set-operator; (2) the continuity of a poset can be characterized by the coincidence of the Scott closure operator and the upper approximation operator induced by the way below relation; (3) meet-continuity can be established from a certain property of the topological closure operator. Additionally, we show how, to each approximating relation, an associated order-compatible topology can be defined in such a way that for the case of a continuous poset the topology associated to the way-below relation is exactly the Scott topology. A preliminary investigation is carried out on this new topology.<\/jats:p><jats:p>Comment: 17 pages; 1figure, Domains XII Workshop<\/jats:p>","DOI":"10.23638\/lmcs-14(2:6)2018","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:03Z","timestamp":1743701283000},"source":"Crossref","is-referenced-by-count":0,"title":["Domains via approximation operators"],"prefix":"10.23638","volume":"Volume 14, Issue 2","author":[{"given":"Zhiwei","family":"Zou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingguo","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4585-9340","authenticated-orcid":false,"given":"Weng Kin","family":"Ho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2018,4,27]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1607.01164v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1607.01164v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:03Z","timestamp":1743701283000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/1525"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,27]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-14(2:6)2018","relation":{"has-preprint":[{"id-type":"arxiv","id":"1607.01164v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1607.01164v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1607.01164","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1607.01164","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,27]]},"article-number":"1525"}}