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 N0-sn-metric spaces and metric spaces is discussed by special mapping. The following results are equivalent in a sequential space：（1）X is an N0-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 → Xsuch that Nf-1（x） is σ-compact for each x ∈ X. It is the generalization of references [3, 4].