关于CF集族和g-度量性(英文)

ON CF FAMILIES AND g-METRIZABILITY

本文证明了具有CF性的半分层、k—空间是σ—空间。此外还证明了,对于X中子集族,HCF CF HCF;对于k—空间X中闭集族、HCP WHCP CF;对于k′—空间X中子集族,HCP WHCP CF,利用上述结果,本文给出了g—度量性的一些等价刻划。

In this paper, we obtain following results (1) A k - space X is a a- space if and only if X is a scmistratifiable space with ( CF) property. (2) For afamily of subsets of a k'- space X, HCP & WIICP CF . (3) For a family ofclosed subsets of a k-space X, HCP WHCP CF. (4) For a family of subsetsof a space X, HCF CF HCF . Also we characterize g-metrizability by usingabove results.