L-Fuzzy拓扑空间中的δT_(i)-分离性  

δT_(i)-separation in L-Fuzzy topological space

作　　者：刘生云 王小霞[1] 王玉焕 LIU Shengyun;WANG Xiaoxia;WANG Yuhuan(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2024年第3期85-90,96,共7页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学地区基金项目(12261090);陕西省自然科学基础研究计划项目(2018JM1042);延安大学研究生教育创新计划项目(YCX2024048)。

摘　　要：利用δ-开集和δ-远域等概念,对L-Fuzzy拓扑空间中的分离性进行了进一步的推广,定义了δT_(i)-分离性(i=-1,0,1,2,3,4),研究了δT_(i)-分离性的一些等价刻画,证明了δT_(i)-分离性的诸如L-好的推广、遗传性、可乘性、同胚不变性、LFδ-拓扑性质等一系列好的性质,并证明了弱诱导的L-Fuzzy拓扑空间的δT_(i)-分离性与其底空间的δT_(i)-分离性之间的关系。研究结果丰富和发展了分离性理论。The separability in L-Fuzzy topological space is further generalized by using the concepts ofδ-open sets andδ-far-field.δT_(i)-separability(i=-1,0,1,2,3,4)is defined and some equivalent characterizations ofδT_(i)separability are studied,In addition,a series of good properties ofδT_(i)-separability,such as L-good generalization,heritability,multiplicability,homeomorphism invariance,LFδ-topological properties are proved,and proved the relationship between theδT_(i)-separability of weakly induced L-Fuzzy topological spaces and theδT_(i)-separability of their base spaces.The research results enrich and develop the theory of separability.

关 键 词：δ-开集 δ-远域 δT_(i)-分离性 

分 类 号：O189.1[理学—数学]