NL-fuzzy拓扑空间与LF完备映射  

NL-fuzzy Topological Spaces and LF-perfect Mappings

作　　者：王延军[1] WANG Yanjun(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）》2022年第1期94-97,共4页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学基金项目(61763045);陕西省自然科学基础研究计划项目(2020JMG552)。

摘　　要：在L-fuzzy拓扑空间中利用N紧集定义了N紧远域进而定义了NL-fuzzy拓扑空间,并证明了NL-fuzzy拓扑空间是L-fuzzy拓扑空间这一重要结论。同时将fuzzy拓扑空间中的fuzzy完备映射合理的推广到L-fuzzy拓扑空间中,引入了LF完备映射,给出其等价刻画。证明了LF完备映射在L-fuzzy拓扑空间与NL-fuzzy拓扑空间中的许多性质,得出在N紧的、T_(2)的L-fuzzy拓扑空间中LF连续映射和LF完备映射是等价的。从而丰富了已有的结果。N-compact remote neighborhood is defined by means of N-compact set in L-fuzzy topological spaces,and it is proved that NL-fuzzy topological spaces is L-fuzzy topological spaces.Meanwhile,fuzzy perfect mappings in fuzzy topological spaces are extended to L-fuzzy topological spaces.The concept of LF-perfect mappings are introduced with some of their basic properties proved in L-fuzzy and NL-fuzzy topological spaces.Meanwhile,in N compact,T_(2)L-fuzzy topological spaces,LF-continuous mappings and LF-perfect mappings are equivalent.

关 键 词：N紧集 L-FUZZY拓扑空间 NL-fuzzy拓扑空间 LF完备映射 

分 类 号：O189.1[理学—数学]