{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:06Z","timestamp":1753894386862,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T00:00:00Z","timestamp":1641945600000},"content-version":"unspecified","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":[],"abstract":"<jats:p>A $\\sigma$-frame is a poset with countable joins and finite meets in which\nbinary meets distribute over countable joins. The aim of this paper is to show\nthat $\\sigma$-frames, actually $\\sigma$-locales, can be seen as a branch of\nFormal Topology, that is, intuitionistic and predicative point-free topology.\nEvery $\\sigma$-frame $L$ is the lattice of Lindel\\\"of elements (those for which\neach of their covers admits a countable subcover) of a formal topology of a\nspecific kind which, in its turn, is a presentation of the free frame over $L$.\nWe then give a constructive characterization of the smallest (strongly) dense\n$\\sigma$-sublocale of a given $\\sigma$-locale, thus providing a\n\"$\\sigma$-version\" of a Boolean locale. Our development depends on the axiom of\ncountable choice.<\/jats:p>","DOI":"10.46298\/lmcs-18(1:7)2022","type":"journal-article","created":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T17:31:20Z","timestamp":1642095080000},"source":"Crossref","is-referenced-by-count":0,"title":["$\\sigma$-locales in Formal Topology"],"prefix":"10.46298","volume":"Volume 18, Issue 1","author":[{"given":"Francesco","family":"Ciraulo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2022,1,12]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/8952\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/8952\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:17:02Z","timestamp":1687292222000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/4244"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,12]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(1:7)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"1801.09644v5","asserted-by":"subject"},{"id-type":"arxiv","id":"1801.09644v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1801.09644v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1801.09644v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1801.09644","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1801.09644","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2022,1,12]]},"article-number":"4244"}}