两个度量化定理

Two Metrization Theorems

应用可数弱遗传闭包保持族及序列有限覆盖刻画了度量空间，得到了一些有趣的度量化定理．

In this paper,we characterize metric spaces in terms of countably weakly hereditary closurepreserving families (CWHCP) and seguence finit covers.The main results are following:(1) X is metrizable if and only if X is qspace and X has a σCWHCP CS*network.(2) If X is a kspace and if X has a σCWHCP basis,then X is metrizable.(3) X is metrizable of and only if X is a seguence space and there exists a seguence {Gn:n∈N} of closed covers of X such that {Gn∶n∈N} is seguencefinit such that {st(x,Gn:n∈N} is a network of x for every x∈X.