关于X_0-sn-网的一些性质  

Some Properties on X_0-sn-networks

作　　者：刘士琴[1] 

机构地区：[1]衡水学院数学与计算机科学系,河北衡水053000

出　　处：《郑州大学学报（理学版）》2017年第3期5-8,共4页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11301159);广西高校重点实验室项目(2016CSOBDP0004)

摘　　要：拓扑空间中的X_0-sn-弱第一可数空间与X_0-sn-网之间关系密切,拓扑空间X是X_0-sn-弱第一可数空间,且P是X中的一个点可数cs-网,如果P是有限交封闭的,则存在P的一个子族B,使得B是X的一个X_0-sn-网.证明得到以下条件等价:1)X具有点可数X_0-sn-网.2)存在一个度量空间M和一个序列商点可数映射f:M→X.3)存在一个度量空间M和一个序列商s-映射f:M→X,使得对x∈X,都有f-1(x)≤ω.Let a topological space X be an X0-sn-weakly first-countable space,and P be a point-countable cs-network for X. The following results were obtained. If P was closed under finite intersections,then there existsed a subfamily B of P such that B was an X0-sn-network for X. It was also proved that the followings were equivalent for a topological space X： 1） X had a point-countable X0-sn-network. 2） There was a metric space M and a sequentially quotient,countable-to-one map f： M → X. 3） There was a metric space M and a sequentially quotient,s-map f： M → X such that f-1（ x） ≤ ω for each x ∈ X.

关 键 词：X0-sn-网 X0-sn-弱第一可数 CS-网 弱基 

分 类 号：O189.1[理学—数学]