{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T01:27:24Z","timestamp":1772242044005,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T00:00:00Z","timestamp":1502755200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T00:00:00Z","timestamp":1502755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T00:00:00Z","timestamp":1502755200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>For a quantale ${\\sf{V}}$, the category $\\sf V$-${\\bf Top}$ of ${\\sf{V}}$-valued topological spaces may be introduced as a full subcategory of those ${\\sf{V}}$-valued closure spaces whose closure operation preserves finite joins. In generalization of Barr's characterization of topological spaces as the lax algebras of a lax extension of the ultrafilter monad from maps to relations of sets, for ${\\sf{V}}$ completely distributive, ${\\sf{V}}$-topological spaces have recently been shown to be characterizable by a lax extension of the ultrafilter monad to ${\\sf{V}}$-valued relations. As a consequence, ${\\sf{V}}$-$\\bf Top$ is seen to be a topological category over $\\bf Set$, provided that ${\\sf{V}}$ is completely distributive. In this paper we give a choice-free proof that ${\\sf{V}}$-$\\bf Top$ is a topological category over $\\bf Set$ under the considerably milder provision that ${\\sf{V}}$ be a spatial coframe. When ${\\sf{V}}$ is a continuous lattice, that provision yields complete distributivity of ${\\sf{V}}$ in the constructive sense, hence also in the ordinary sense whenever the Axiom of Choice is granted.<\/jats:p>","DOI":"10.23638\/lmcs-13(3:12)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:29:36Z","timestamp":1743686976000},"source":"Crossref","is-referenced-by-count":0,"title":["A Note on the Topologicity of Quantale-Valued Topological Spaces"],"prefix":"10.23638","volume":"Volume 13, Issue 3","author":[{"given":"Hongliang","family":"Lai","sequence":"first","affiliation":[]},{"given":"Walter","family":"Tholen","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,8,15]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1612.09504v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1612.09504v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:29:36Z","timestamp":1743686976000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2640"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,15]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(3:12)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1612.09504v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.09504v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1612.09504","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1612.09504","asserted-by":"subject"}],"is-cited-by":[{"id-type":"doi","id":"10.3934\/math.2022513","asserted-by":"object"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,15]]},"article-number":"2640"}}