{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T07:40:06Z","timestamp":1750664406641,"version":"3.41.0"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"UGC India","award":["16-6 (December 2017)\/2018 (NET\/CSIR)"],"award-info":[{"award-number":["16-6 (December 2017)\/2018 (NET\/CSIR)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:p> This paper explores the topological aspects of algebras determined by rough sets. It is well known that the lattice structure of rough sets is characterized by the lattices of the form [Formula: see text]. We show that algebras determined by the rough sets are characterized by the condition \u201cany chain of completely prime filters has at most two elements\u201d. We introduce the notion of rough topological space in which the basic open set has at most two elements. We further provide representations of rough topological spaces in terms of topologies determined by algebras of rough sets. <\/jats:p>","DOI":"10.1142\/s1793005725500309","type":"journal-article","created":{"date-parts":[[2024,3,22]],"date-time":"2024-03-22T15:09:05Z","timestamp":1711120145000},"page":"661-675","source":"Crossref","is-referenced-by-count":0,"title":["Rough Sets: A Topological View"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2479-432X","authenticated-orcid":false,"given":"Arun","family":"Kumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-3027-5381","authenticated-orcid":false,"given":"Shilpi","family":"Kumari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,4,20]]},"reference":[{"key":"S1793005725500309BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"S1793005725500309BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18859-6_7"},{"key":"S1793005725500309BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-016-9696-6"},{"key":"S1793005725500309BIB004","first-page":"3","volume-title":"Rough Fuzzy Hybridization: A New Trend in Decision-making","author":"Komorowski J.","year":"1999"},{"key":"S1793005725500309BIB005","first-page":"495","volume":"36","author":"Pomyka\u0142a J.","year":"1988","journal-title":"Bulletin of the Polish Academy of Sciences. 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Heyting,  Die Formalen Regeln der Intuitionistischen Logik, I, II, III,  Sitzungsberichte der Preu\u00dfischen Akademie der Wissenschaften. Physikalisch-Mathematische Klasse  (De\u00fctsche Akademie der Wissenschaften zu Berlin, 1930),  pp. 42\u201356,  57\u201371, 158\u2013169 (in German)."},{"key":"S1793005725500309BIB014","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1958-0095135-X"},{"key":"S1793005725500309BIB015","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809088"},{"key":"S1793005725500309BIB016","volume-title":"Lattice Theory","volume":"25","author":"Birkhoff G.","year":"1995","edition":"3"},{"volume-title":"An Algebraic Approach to Non-classical Logics","year":"1974","author":"Rasiowa H.","key":"S1793005725500309BIB017"},{"volume-title":"The Mathematics of Metamathematics","year":"1963","author":"Rasiowa H.","key":"S1793005725500309BIB018"},{"key":"S1793005725500309BIB019","first-page":"359","volume":"11","author":"Monteiro A.","year":"1963","journal-title":"Bulletin de L\u2019Acad\u00e9mie Polonaise Des Sciences: S\u00e9rie des Sciences Math\u00e9matiques, Astronomiques, et Physiques"}],"container-title":["New Mathematics and Natural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793005725500309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T07:10:06Z","timestamp":1750662606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793005725500309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,20]]},"references-count":19,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["10.1142\/S1793005725500309"],"URL":"https:\/\/doi.org\/10.1142\/s1793005725500309","relation":{},"ISSN":["1793-0057","1793-7027"],"issn-type":[{"type":"print","value":"1793-0057"},{"type":"electronic","value":"1793-7027"}],"subject":[],"published":{"date-parts":[[2024,4,20]]}}}