{"title":"(a)拓扑空间中Star-Semi-Lindelöfness的选择版本","authors":"Sheetal Luthra, Harsh V. S. Chauhan, B. Tyagi","doi":"10.2478/tmmp-2022-0002","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we deal with the properties (a)R-star-semi-Lindelöf and (a)M-star-semi-Lindelöf in (a)topological spaces. These properties are interesting as every (a)Rs-separable space is (a)R-star-semi-Lindelöf and every (a)s-semi-Lindelöf space is (a)R-star-semi-Lindelöf but not every (a)R-star-semi-Lindelöf space is (a)Rs-separable or (a)s-semi-Lindelöf. It is shown that if an (a)topological space X is the union of countably many (a)-open and (a)Rstar-semi-Lindelöf subspaces, then X is (a)R-star-semi-Lindelöf. Similar results are obtained in the context of (a)M-star-semi-Lindelöf spaces. Further, suitable and required counterexamples are given.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"81 1","pages":"39 - 56"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Selective Version of Star-Semi-Lindelöfness in (a) Topological Spaces\",\"authors\":\"Sheetal Luthra, Harsh V. S. Chauhan, B. Tyagi\",\"doi\":\"10.2478/tmmp-2022-0002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we deal with the properties (a)R-star-semi-Lindelöf and (a)M-star-semi-Lindelöf in (a)topological spaces. These properties are interesting as every (a)Rs-separable space is (a)R-star-semi-Lindelöf and every (a)s-semi-Lindelöf space is (a)R-star-semi-Lindelöf but not every (a)R-star-semi-Lindelöf space is (a)Rs-separable or (a)s-semi-Lindelöf. It is shown that if an (a)topological space X is the union of countably many (a)-open and (a)Rstar-semi-Lindelöf subspaces, then X is (a)R-star-semi-Lindelöf. Similar results are obtained in the context of (a)M-star-semi-Lindelöf spaces. Further, suitable and required counterexamples are given.\",\"PeriodicalId\":38690,\"journal\":{\"name\":\"Tatra Mountains Mathematical Publications\",\"volume\":\"81 1\",\"pages\":\"39 - 56\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tatra Mountains Mathematical Publications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/tmmp-2022-0002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tatra Mountains Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/tmmp-2022-0002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Selective Version of Star-Semi-Lindelöfness in (a) Topological Spaces
Abstract In this paper, we deal with the properties (a)R-star-semi-Lindelöf and (a)M-star-semi-Lindelöf in (a)topological spaces. These properties are interesting as every (a)Rs-separable space is (a)R-star-semi-Lindelöf and every (a)s-semi-Lindelöf space is (a)R-star-semi-Lindelöf but not every (a)R-star-semi-Lindelöf space is (a)Rs-separable or (a)s-semi-Lindelöf. It is shown that if an (a)topological space X is the union of countably many (a)-open and (a)Rstar-semi-Lindelöf subspaces, then X is (a)R-star-semi-Lindelöf. Similar results are obtained in the context of (a)M-star-semi-Lindelöf spaces. Further, suitable and required counterexamples are given.
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