{"title":"θ空间","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":"{\"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}","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}
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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