RL-fuzzy拓扑及其模糊紧性

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英文篇名：RL-fuzzy topology and the related fuzzy compactness 作者：李宏艳 ; 李清华 英文作者：LI Hong-yan;LI Qing-hua;School of Mathematics and Information Science,Shandong Technology and Business University;School of Mathematics and Information Science,Yantai University; 关键词：RL-拓扑 ; RL-fuzzy拓扑 ; RL-fuzzy紧 ; RL-fuzzy连续 英文关键词：RL-topology;;RL-fuzzy topology;;RL-fuzzy compactness;;RL-fuzzy continuous 中文刊名：SDDX 英文刊名：Journal of Shandong University(Natural Science) 机构：山东工商学院数学与信息科学学院;烟台大学数学与信息科学学院; 出版日期：2018-12-04 11:48 出版单位：山东大学学报(理学版) 年：2019 期：v.54 基金：国家自然科学基金资助项目(11471297);; 山东省高等学校科学技术计划项目(J18KA245) 语种：中文; 页：SDDX201902004 页数：7 CN：02 ISSN：37-1389/N 分类号：55-60+69

摘要

提出了L-子集A(L是完全分配的De Morgan代数)中伪补的概念并研究了它的性质,以此为基础给出了A上RL-fuzzy拓扑的定义,使得Kubiak和ostak意义下的L-fuzzy拓扑和A上RL-拓扑是该拓扑的特殊情形。进一步地研究了RL-fuzzy拓扑空间的RL-fuzzy紧性,得到了2个RL-fuzzy紧集的并仍是RL-fuzzy紧集,一个RL-fuzzy紧集和一个RL-fuzzy闭集的交仍是RL-fuzzy紧集,RL-fuzzy紧性是连续不变性等结论。
        The concept of pseudo-complement on an L-subset A is defined and studied,where L is a completely distributive De Morgan algebra. Based on this newconcept,the definition of RL-fuzzy topology on A is introduced. The L-fuzzy topology in sense of Kubiak and ostak and the RL-topology on A are special cases of this kind of topology. The RL-fuzzy compactness of RL-fuzzy topological spaces is further studied. The union of two RL-fuzzy compact sets is RL-fuzzy compact. The intersection of an RL-fuzzy compact set and an RL-fuzzy closed set is RL-fuzzy compact. The RL-fuzzy compactness is an invariant under RL-fuzzy continuous maps.

引文

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