{"title":"θ-spaces","authors":"Peter Fletcher, William F. Lindgren","doi":"10.1016/0016-660X(78)90059-4","DOIUrl":null,"url":null,"abstract":"<div><p>This paper studies the relationships of θ-spaces to other generalized metric spaces. In particular, a condition shared by θ-spaces and spaces with a quasi-<em>G<sub>g</sub></em> diagonal is introduced, and it is shown that every regular θ refinable β-space satisfying this condition is semi-stratifiable. In addition, a regular quasi-complete space satisfying this condition has a base of countable order.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 2","pages":"Pages 139-153"},"PeriodicalIF":0.0000,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90059-4","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X78900594","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies the relationships of θ-spaces to other generalized metric spaces. In particular, a condition shared by θ-spaces and spaces with a quasi-Gg diagonal is introduced, and it is shown that every regular θ refinable β-space satisfying this condition is semi-stratifiable. In addition, a regular quasi-complete space satisfying this condition has a base of countable order.
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