【摘要】 本文引入弱基g-函数的概念,利用它给出拓扑空间度量化的一些等价刻画。证明了拓扑空间X可以度量化,当且仅当X有弱基g-函数满足(s)和(g2)(或(ks)和g1)条件。另外,本文还给出了J.Nagata两个定理的简单证明。更多还原

【Abstract】 In this paper, we introduce the weak-base g-function, and give some characterizations of metrizability of topological spaces in terms of weak-base gr-functons. We proved that a space X is metrizable iff it has a weak base g-function satisfying conditions (s) and g2 (or (ks) and gl). And we shall give immediate proofs of two theorems proved by J. Nagata.更多还原