局部可分度量空间闭s映象的注记

数学物理学报

局部可分度量空间闭s映象的注记

林寿; 燕鹏飞

(漳州师范学院数学系漳州 363000)
(宁德师范高等专科学校数学研究所宁德 352100)

收稿日期:2005-03-15 修回日期:2006-01-08 出版日期:2007-02-25 发布日期:2007-02-25
通讯作者: 林寿
基金资助:
国家自然科学基金(10571151)和福建省自然科学基金(2006J0397)资助

A Note on Closed s-images of Locally Separable Metric Spaces

Lin Shou; Yan Pengfei

Department of Mathematics, Zhangzhou Teachers' College, Zhangzhou 363000;
Institute of Mathematics, Ningde Teachers' College, Ningde 352100

Received:2005-03-15 Revised:2006-01-08 Online:2007-02-25 Published:2007-02-25
Contact: Lin Shou

摘要/Abstract

摘要： 该文讨论局部可分度量空间闭s映象的分解定理, 证明了正则的Fréchet空间是局部可分度量空间的闭s映象当且仅当满足如下条件: 具有点可数的cs*网, 第一可数的闭子空间是局部可分的, 且Lindelof的闭子空间是可分的.

关键词: cs*网, wcs*网, 闭映射, s映射, N₁紧性, 可分性, Lindelof 性

Abstract: In this note a decomposition theorem about closed s-images of locally separable metric spaces is discussed. It is showed that a regular Fréchet space is a closed s-image of a locally separable metric space if and only if it has a point-countable cs*-network, each first countable closed subset is locally separable, and each Lindelof closed subset is separable.

Key words: cs*-networks, wcs*-networks, Closed mappings, s-mappings,
N₁-compactness, Separability, Lindelofness

中图分类号:

54E35

林寿; 燕鹏飞. 局部可分度量空间闭s映象的注记[J]. 数学物理学报, 2007, 27(1): 171-175.

Lin Shou; Yan Pengfei. A Note on Closed s-images of Locally Separable Metric Spaces[J]. Acta mathematica scientia,Series A, 2007, 27(1): 171-175.