I(L)型诱导空间的可数性

The Countability of Induced I(L) -fuzzy Topological Spaces

本文证明了(L^X,δ)与其I(L)型诱导空间(I(L)~X,ω(δ))的权,特征,浓度.Lindelof度相等,(L^X,δ)为Lindelof空间当且仅当(I(L)~X,σ(δ))为Lindelof空间,且给出了(L^X,δ)与(I(L^X)ω(δ))的稠密集,稀疏集,第一纲集,第二纲集,Baire性质之间的关系.

In this paper, we prove that the weight, character, density, and Lindclof degree of (LX,δ) are equal with those of (I(L)x,ω(δ)) , and that (Lx,δ) is a Lindelof space if and only if (I(L)x,ω(δ)) is a Lindelof space. We also compare (Lx,δ) and (I(L)x,ω(δ)) in respects of the dense set, nowhere dense set, first category set, second category set and Baire property, respectively.