L-拓扑空间的半S_β-紧性

Semi-S_β-compactness in L-topological Spaces

在L-拓扑空间中引入半Sβ-紧性,这种紧性是针对任意L-模糊子集定义的,它是Sβ-紧性的推广。研究半Sβ-紧性的性质,如一个半Sβ-紧集与一个半闭集的交仍为半Sβ-紧的;半Sβ-紧性在不定映射下保持不变;由分明拓扑空间(X,τ)拓扑生成的L-拓扑空间(LX,ωL(τ))是半Sβ-紧的当且仅当(X,τ)是半紧的。此外,还给出了半Sβ-紧性的网式刻画。

In this paper,the notion of semi-Sβ-compactness is introduced in L-topological spaces.This compactness is defined for arbitrary L-fuzzy subsets and it is a generalization of Sβ-compactness.Some properties of the semi-Sβ-compactness is investigated,it is found that： the intersection of a semi-Sβcompact set and a semiclosed set is still semi-Sβ-compact;the semiSβ-compactness is preserved under irresolute mapping;the L-topological space （LX,ωL（τ）） generating by（X,τ） is semi-Sβ-compact if and only if（X,τ） is semi-compact.Moreover,the semi-Sβ-compactness can also be characterized by nets.