{"title":"连续双拓扑空间的可分性准则","authors":"O. Ogola, N. B. Okelo, O. Ongati","doi":"10.30538/psrp-oma2021.0091","DOIUrl":null,"url":null,"abstract":"In this paper, we give characterizations of separation criteria for bitopological spaces via \\(ij\\)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let \\((X, \\tau_{1}, \\tau_{2})\\) be a \\(T_{0}\\) space then, the property of \\(T_{0}\\) is topological and hereditary. Similarly, when \\((X, \\tau_{1}, \\tau_{2})\\) is a \\(T_{1}\\) space then the property of \\(T_{1}\\) is topological and hereditary. Next, we show that separation axiom \\(T_{0}\\) implies separation axiom \\(T_{1}\\) which also implies separation axiom \\(T_{2}\\) and the converse is true.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On separability criteria for continuous Bitopological spaces\",\"authors\":\"O. Ogola, N. B. Okelo, O. Ongati\",\"doi\":\"10.30538/psrp-oma2021.0091\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give characterizations of separation criteria for bitopological spaces via \\\\(ij\\\\)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let \\\\((X, \\\\tau_{1}, \\\\tau_{2})\\\\) be a \\\\(T_{0}\\\\) space then, the property of \\\\(T_{0}\\\\) is topological and hereditary. Similarly, when \\\\((X, \\\\tau_{1}, \\\\tau_{2})\\\\) is a \\\\(T_{1}\\\\) space then the property of \\\\(T_{1}\\\\) is topological and hereditary. Next, we show that separation axiom \\\\(T_{0}\\\\) implies separation axiom \\\\(T_{1}\\\\) which also implies separation axiom \\\\(T_{2}\\\\) and the converse is true.\",\"PeriodicalId\":52741,\"journal\":{\"name\":\"Open Journal of Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Open Journal of Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30538/psrp-oma2021.0091\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Journal of Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30538/psrp-oma2021.0091","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On separability criteria for continuous Bitopological spaces
In this paper, we give characterizations of separation criteria for bitopological spaces via \(ij\)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let \((X, \tau_{1}, \tau_{2})\) be a \(T_{0}\) space then, the property of \(T_{0}\) is topological and hereditary. Similarly, when \((X, \tau_{1}, \tau_{2})\) is a \(T_{1}\) space then the property of \(T_{1}\) is topological and hereditary. Next, we show that separation axiom \(T_{0}\) implies separation axiom \(T_{1}\) which also implies separation axiom \(T_{2}\) and the converse is true.