两个度量化定理  

Two Metrization Theorems

作　　者：胡洪萍[1,2,3] 宋际平 张运良[1,2,3] 

机构地区：[1]西安联合大学师范学院 [2]四川乐山师范专科学校 [3]西安培华女子大学

出　　处：《纺织高校基础科学学报》1998年第2期174-176,共3页Basic Sciences Journal of Textile Universities

摘　　要：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.

关 键 词：CS-网 可数弱遗传 闭包保持族 网络 

分 类 号：O189[理学—数学]