{"title":"单位的Lg-fuzzy划分","authors":"Marzieh Mostafavi","doi":"10.56827/jrsmms.2022.1001.11","DOIUrl":null,"url":null,"abstract":"In this paper, we define LGc-fuzzy Euclidean topological space with countable basis, which L denotes a complete distributive lattice and we show that each LGc-fuzzy open covering of this space can be refined to an LGc-fuzzy open covering that is locally finite. We introduce C∞ LG-fuzzy manifold (X, Tc), with countable basis of LG-fuzzy open sets which X is an L-fuzzy subset of a crisp set M and T : LMX → L, is an L-gradation of openness on X. We prove that for any LG-fuzzy topological manifold (X,T), there exists an LG-fuzzy exhaustion. We prove LG-Urysohn lemma and also existence of LG-partitions of unity on every LG-fuzzy topological manifold.","PeriodicalId":282200,"journal":{"name":"JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"156 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"LG-FUZZY PARTITION OF UNITY\",\"authors\":\"Marzieh Mostafavi\",\"doi\":\"10.56827/jrsmms.2022.1001.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we define LGc-fuzzy Euclidean topological space with countable basis, which L denotes a complete distributive lattice and we show that each LGc-fuzzy open covering of this space can be refined to an LGc-fuzzy open covering that is locally finite. We introduce C∞ LG-fuzzy manifold (X, Tc), with countable basis of LG-fuzzy open sets which X is an L-fuzzy subset of a crisp set M and T : LMX → L, is an L-gradation of openness on X. We prove that for any LG-fuzzy topological manifold (X,T), there exists an LG-fuzzy exhaustion. We prove LG-Urysohn lemma and also existence of LG-partitions of unity on every LG-fuzzy topological manifold.\",\"PeriodicalId\":282200,\"journal\":{\"name\":\"JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"volume\":\"156 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56827/jrsmms.2022.1001.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56827/jrsmms.2022.1001.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we define LGc-fuzzy Euclidean topological space with countable basis, which L denotes a complete distributive lattice and we show that each LGc-fuzzy open covering of this space can be refined to an LGc-fuzzy open covering that is locally finite. We introduce C∞ LG-fuzzy manifold (X, Tc), with countable basis of LG-fuzzy open sets which X is an L-fuzzy subset of a crisp set M and T : LMX → L, is an L-gradation of openness on X. We prove that for any LG-fuzzy topological manifold (X,T), there exists an LG-fuzzy exhaustion. We prove LG-Urysohn lemma and also existence of LG-partitions of unity on every LG-fuzzy topological manifold.