{"title":"Convergence in fuzzy topological spaces","authors":"R. Lowen","doi":"10.1016/0016-660X(79)90004-7","DOIUrl":null,"url":null,"abstract":"<div><p>In the first paragraph we study filters in the lattice <em>I</em><sup><em>X</em></sup>, where <em>I</em> is the unitinterval and <em>X</em> an arbitrary set. The main result of this section is a characterization of minimal prime filters in <em>I</em><sup><em>X</em></sup> containing a given filter in <em>I</em><sup><em>X</em></sup> by means of ultrafilters on <em>X</em>.</p><p>In the second paragraph we apply the results of the previous section to define convergence in a fuzzy topological space which enables us to characterize fuzzy compactness and fuzzy continuity.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 2","pages":"Pages 147-160"},"PeriodicalIF":0.0000,"publicationDate":"1979-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90004-7","citationCount":"180","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X79900047","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 180
Abstract
In the first paragraph we study filters in the lattice IX, where I is the unitinterval and X an arbitrary set. The main result of this section is a characterization of minimal prime filters in IX containing a given filter in IX by means of ultrafilters on X.
In the second paragraph we apply the results of the previous section to define convergence in a fuzzy topological space which enables us to characterize fuzzy compactness and fuzzy continuity.
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