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| 摘要: |
| 本文研究了ℵ0-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ℵ0-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. |
| 关键词: ℵ0-sn-度量空间 可数对一 序列商映射 |
| DOI： |
| 分类号:O189.1 |
| 基金项目:地区基金资助(11061004);广西青年自然科学基金资助(2014GXNSFBA118015);玉林师范学院重点项目基金资助(2012YJZD20). |
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| COUNTABLE TO ONE MAPS AND RELATED MATTERS |
|
WANG Pei
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| Abstract: |
| In this paper,the connection between ℵ0-sn-metric spaces and metric spaces is discussed by special mapping.The following results are equivalent in a sequential space:(1)X is an ℵ0-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]. |
| Key words: ℵ0-sn-metric space countable to one sequentially quotient map |
