L-拓扑空间中的可数PS-紧性及PS-Lindelf性质

Countable PS-compactness and PS-Lindelf Property in L-topological Spaces

在L-拓扑空间中借助于准半开L-集及其不等式给出了可数PS-紧性和PS-Lindelf性质的新定义,这里L是完备的DeMorgan代数.同时认为可数PS-紧性和PS-Lindelf性质也能够借助于准半闭L-集及其不等式刻画.当L是完全分配的DeMorgan代数时,给出了可数PS-紧性和PS-Lindelf性质的更深层特征.

A new definition of PS-compactness and PS-Lindelf property is presented in L-topological spaces by means of pre-semiopen L-sets and their inequality,where L is a complete DeMorgan algebra.The new definition can also be characterized by means of pre-semiclosed L-sets and their inequality.When L is a completely distributive DeMorgan algebra,the futher characterizations of countable PS-compactness and PS-Lindelf property are given.