可数对一映射及相关问题
COUNTABLE TO ONE MAPS AND RELATED MATTERS

本文研究了？0-sn-度量空间与度量空间之间的关系.利用特殊映射,获得了在序列空间中下述命题等价:(1)空间X是？0-sn-度量空间;(2)存在从度量空间M到X可数对一、序列商、σ映射f;(3)存在从度量空间M到X可数对一、序列商、σ映射f使得对每一个x ∈ X,？f-1(x)是σ-紧.推广了参考文献[3,4]中的一些结果.
In this paper,the connection between ？0-sn-metric spaces and metric spaces is discussed by special mapping.The following results are equivalent in a sequential space:(1)X is an ？0-sn-metric spaces;(2) There is a metric spaces M and countable to one、sequentially quotient、σ map f:M→X;(3) There is a metric spaces M and countable to one、sequentially quotient、σ map f:M→X such that ？f-1(x) is σ-compact for each x ∈ X.It is the generalization of references [3,4]