模糊化拓扑空间中的δ-分离性及范畴FδTop的拓扑性  

δ-separability in fuzzifying topological space and topology of category FδTop

作　　者：刘生云 王小霞[1] 王玉焕 LIU Shengyun;WANG Xiaoxia;WANG Yuhuan(School 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学院,陕西延安716000

出　　处：《湖北大学学报（自然科学版）》2024年第3期424-432,共9页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(12261090);陕西省自然科学基础研究计划项目(2018JM1042)资助。

摘　　要：在模糊化拓扑空间中,利用连续值逻辑语义的方法介绍δ-开集,δ-闭集,δ-闭包和δ-邻域的概念,并以此为工具阐述T_(1)^(δ),T_(2)^(δ),T_(3)^(δ),T_(4)^(δ),T_(3)^(Sδ),T_(4)^(Sδ)分离性公理;其次研究它们的一些特征及等价刻画,讨论并证明它们彼此之间的关系;最后通过对δ-连续映射的定义,证明范畴FδTop是范畴Set上的拓扑范畴。The concepts of δ-open set,δ-closed set,δ-closure and δ-neighborhood were introduced by using the method of continuous valued logical semantics in fuzzifying topological space,and the axiom of T_(1)^(δ),T_(2)^(δ),T_(3)^(δ),T_(4)^(δ),T_(3)^(Sδ),T_(4)^(Sδ) separation was expounded with this method.Secondly,some of their features and equivalent characterizations were studied,then discussed and proved their relationship with each other.Finally,category FδTop was proved to be a topological category on category Set by defining δ-continuous mapping.

关 键 词：逻辑语义 模糊化拓扑空间 δ-开集 δ_(i)-分离性 拓扑范畴 

分 类 号：O189.1[理学—数学]