L-fuzzy拓扑空间的相对近似PS紧性

Relative Near PS-Compact L-subsets

本文在LF拓扑空间中引入了一种新的相对紧性—相对近似PS紧性,给出了相对近似PS紧性的α-网、r-PS覆盖、r-有限交性质等多种刻画。探讨了相对近似PS紧性和近似PS紧性之间的关系,即:近似PS紧性蕴含相对近似PS紧性;近似PS紧空间中的每个LF集是相对近似PS紧的。相对近似PS紧性还具有以下的性质:任两个相对近似PS紧集的并是相对近似PS紧;任一族相对近似PS紧集的交是相对近似PS紧的。最后,证明了相对近似PS紧性在PS连续映射下保持不变。由于相对近似PS紧性是针对任意LF子集来定义的,且保持了一般拓扑空间中紧性的许多好的性质,所以是紧性理论的一种较为理想的推广。

In this paper the new concept of relative near PS-compactness in L-fuzzy topological spaces is introduced. The relative near PS-eompactness is described with α-net, r-ps-cover, r-finite intersection property. The relationship between relative near PS-compactness and near PS-compactness is investigated. It is found that near PS-compactness implies relative near PS-eompaetness and every LF- set of near PS-eompact space is relative near PS-compaet. The relative near PS-eompactness possess the following properties ： the union of two arbitrary relative near PS-compact sets is relative near PS-eompact; the intersection of a family relative near PS-eompaet sets is also relative near PS-compact. Finally, it is proved that the relative near PS-compaetness is invariant under the PS-continuous maps. This relative near PS-compactness is defined for arbitrary L-fuzzy subsets, and it preserves many good properties of compactness in general topological spaces.