RL-fuzzy拓扑及其模糊紧性

RL-fuzzy topology and the related fuzzy compactness

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 Sostak 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.