NL-Fuzzy拓扑空间的连通性  

Connectedness in NL-Fuzzy topological spaces

作　　者：高佳欣 王小霞[1] 李乔乔 GAO Jiaxin;WANG Xiaoxia;LI Qiaoqiao(College of Mathematics and Compute 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）》2023年第4期112-114,120,共4页Journal of Yan'an University：Natural Science Edition

基　　金：陕西省自然科学基础研究项目(2018JM1042)。

摘　　要：主要通过类比推理和文献分析法,将L-Fuzzy拓扑空间中的连通性引入到NL-Fuzzy拓扑空间中。首先,基于N-开集、N-闭包等概念定义了N-连通性,给出了其等价刻画,讨论了它的一些基本性质;其次,证明了N-连通性具有可和性和拓扑不变性,以及若可拓扑生成的LF拓扑空间是N-连通的,则分明拓扑空间也是N-连通,并通过反例证明了N-连通性不是L-好的推广。研究结果丰富了L-Fuzzy拓扑空间理论体系,为NL-Fuzzy拓扑空间的相关理论研究提供了一定的参考价值。In this paper,connectedness in L-Fuzzy topological spaces is introduced into NL-Fuzzy topological spaces by analogical reasoning and literature analysis.Firstly,we defined N-connectedness in NL-Fuzzy topologi⁃cal spaces based on N-open set and N-closure,and gave its equivalent characterizations,and discussed some of its basic properties.Then,we proved that N-connectedness has additive property and topological invariance.If the topologically generated LF topological space was N-connected,then the clear topological space would also be N-connected.We also proved that N-connectedness is not a L-good generalization through counterexamples.The research enriches the theoretical system of L-Fuzzy topological spaces and provides reference for the theoretical research of NL-Fuzzy topological Spaces.

关 键 词：NL-Fuzzy拓扑空间 N-连通性 拓扑不变性 L-好的推广 

分 类 号：O189[理学—数学]