I(L)型诱导空间的可数性

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

中文关键词:  I（L）型诱导空间  权  特征  浓度  Lindel?f度

英文关键词:induced I（L） -fuzzy topological spaces  weight  character  density  Lindeld?f degree.

中文摘要:

      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.Lindel?f度相等,(L^X,δ)为Lindel?f空间当且仅当(I(L)^X,σ(δ))为Lindel?f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.

英文摘要:

      In this paper, we prove that the weight, character, density, and Lindcl?f degree of (L^X,δ) are equal with those of (I(L)^X,ω(δ)) , and that (L^X,δ) is a Lindel?f space if and only if (I(L)^X,ω(δ)) is a Lindelof space. We also compare (L^X,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.