{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:18:08Z","timestamp":1773145088300,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T00:00:00Z","timestamp":1553212800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T00:00:00Z","timestamp":1553212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T00:00:00Z","timestamp":1553212800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["731143"],"award-info":[{"award-number":["731143"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling with an attempt to formulate a topological version of the Scott Convergence Theorem, i.e., an order-theoretic characterisation of those posets for which the Scott-convergence $\\mathcal{S}$ is topological. To do this, we make use of the $\\mathcal{ID}$ replacement principle to create topological analogues of well-known domain-theoretic concepts, e.g., $\\mathcal{I}$-continuous spaces correspond to continuous posets, as $\\mathcal{I}$-convergence corresponds to $\\mathcal{S}$-convergence. In this paper, we consider two novel topological concepts, namely, the $\\mathcal{I}$-stable spaces and the $\\mathcal{DI}$ spaces, and as a result we obtain some necessary (respectively, sufficient) conditions under which the convergence structure $\\mathcal{I}$ is topological.<\/jats:p>","DOI":"10.23638\/lmcs-15(1:29)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:01Z","timestamp":1743701281000},"source":"Crossref","is-referenced-by-count":1,"title":["Topological Scott Convergence Theorem"],"prefix":"10.23638","volume":"Volume 15, Issue 1","author":[{"given":"Hadrian","family":"Andradi","sequence":"first","affiliation":[]},{"given":"Weng Kin","family":"Ho","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,3,22]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1710.03115v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1710.03115v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:01Z","timestamp":1743701281000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/1526"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,22]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(1:29)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1710.03115v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1710.03115v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1710.03115v1","asserted-by":"subject"},{"id-type":"arxiv","id":"1607.01146v1","asserted-by":"subject"}],"has-review":[{"id-type":"uri","id":"https:\/\/zbmath.org\/7056217","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1710.03115","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1710.03115","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,22]]},"article-number":"1526"}}