{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T02:18:31Z","timestamp":1648779511833},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2020,11]]},"abstract":"<jats:p> In this paper, we introduce soaker filters in a residuated lattice, give some characterizations and investigate some properties of them. Then we define a topology on the set of all the soaker filters, which we call reflectional topology, show it is an Alexandrov topology and give a basis for it. We introduce the notion of join-soaker filters and prove that when the residuated lattice is a join-soaker filter, then the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we prove the reflectional topology is [Formula: see text], give necessary and sufficient conditions under which it is [Formula: see text] and prove that being [Formula: see text] is equivalent to being [Formula: see text]. Several illustrative examples are given. <\/jats:p>","DOI":"10.1142\/s1793005720500362","type":"journal-article","created":{"date-parts":[[2020,12,1]],"date-time":"2020-12-01T12:08:26Z","timestamp":1606824506000},"page":"593-608","source":"Crossref","is-referenced-by-count":0,"title":["Reflectional Topology in Residuated Lattices"],"prefix":"10.1142","volume":"16","author":[{"given":"F.","family":"Forouzesh","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and computing, Higher Education Complex of Bam, Iran"},{"name":"Department of Pure Mathematics, Shahid Bahonar University of Kerman, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. N.","family":"Hosseini","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and computing, Higher Education Complex of Bam, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,11,30]]},"reference":[{"key":"S1793005720500362BIB001","first-page":"47","volume":"56","author":"Krull W.","year":"1924","journal-title":"Sitzungsberichte der physikalisch medizinischen Societad der Erlangen"},{"key":"S1793005720500362BIB002","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1090\/S0002-9947-1939-0000230-5","volume":"46","author":"Dilworth R. P.","year":"1939","journal-title":"Transactions of the American Mathematical Society"},{"key":"S1793005720500362BIB003","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1090\/S0002-9947-1939-1501995-3","volume":"45","author":"Ward M.","year":"1939","journal-title":"Transactions of the American Mathematical Society"},{"key":"S1793005720500362BIB004","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1215\/S0012-7094-40-00649-4","volume":"6","author":"Ward M.","year":"1940","journal-title":"Duke Mathematical Journal"},{"key":"S1793005720500362BIB005","volume-title":"Distributive Lattices","author":"Balbes R.","year":"1974"},{"key":"S1793005720500362BIB006","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1002\/malq.19790250706","volume":"25","author":"Pavelka J.","year":"1979","journal-title":"Zeitschrift fur mathematische Logik und Grundlagen der Mathematik"},{"key":"S1793005720500362BIB008","series-title":"Trends in Logic-Studia Logica Library","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-5300-3","volume-title":"Metamathematics of Fuzzy Logic","volume":"4","author":"Hajek P.","year":"1998"},{"key":"S1793005720500362BIB010","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/s001530100088","volume":"40","author":"Turunen E.","year":"2001","journal-title":"Archive for Mathematical Logic"},{"key":"S1793005720500362BIB012","doi-asserted-by":"crossref","first-page":"2165","DOI":"10.1007\/s00500-012-0884-7","volume":"16","author":"Haveshki M.","year":"2012","journal-title":"Soft Computing"},{"key":"S1793005720500362BIB013","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1007\/s00500-015-1620-x","volume":"19","author":"He P.","year":"2015","journal-title":"Soft Computing"},{"key":"S1793005720500362BIB014","volume-title":"Algebras of Logic as BCK Algebras","author":"Iorgulescu A.","year":"2008"}],"container-title":["New Mathematics and Natural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793005720500362","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,1]],"date-time":"2020-12-01T12:09:04Z","timestamp":1606824544000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793005720500362"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11]]},"references-count":11,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["10.1142\/S1793005720500362"],"URL":"https:\/\/doi.org\/10.1142\/s1793005720500362","relation":{},"ISSN":["1793-0057","1793-7027"],"issn-type":[{"value":"1793-0057","type":"print"},{"value":"1793-7027","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11]]}}}