L－fuzzy拓扑空间的弱紧性  

The Weak Compactness in L-fuzzy Topological Space

作　　者：李生刚[1] 

机构地区：[1]陕西师范大学数学系

出　　处：《工程数学学报》1995年第4期94-98,共5页Chinese Journal of Engineering Mathematics

摘　　要：本文定义了ＬＦ拓扑空间的弱紧性，并借助于网和滤子的念对此进行了刻划；证明了弱紧性是对闭子集遗传的、被连续Ｌ值Ｚａｄｅｈ型函数保持的性质，作为弱紧性的一种应用，刻划了链和弱紧格，找出了良紧性与强Ｆ紧性和Ｆ紧性的差别，证明了在弱紧空间类中，基于良紧性、强Ｆ紧性和Ｆ紧性定义的三种Ⅰ型仿紧性（分别地：Ⅱ型仿紧性，Ｌｉｎｄｅｌｆｆ特性）彼此等价。Abstract The weak compactness in L-fuzzy topological spaces is defined and characterized in terms of nets and filters.It proves that the weak cmpactness is hereditery with respect to closed subsets,and an invariant of fuzzy continuous mapping.As a kind of application,it characterizes chains,weakly compact lattice and algebraic lattice,finds out the difference between N-compactness and strong F-compactness(resp.,F-compactness),and proves that the three kinds of l-paracompactness(resp.,2-paracompactness,Lindelof properties),defined on N-compactness,strong F-compactness and F-compactness respectively,are eqivalent in the class of all weakly compact spaces.

关 键 词：良紧性 强F紧性 F紧性 弱紧性 LF拓扑空间 

分 类 号：O159[理学—数学] O189.1[理学—基础数学]