点星网与度量空间的映像

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点星网与度量空间的映像林寿¹, 黄燕晖², 张静²1. 宁德师范学院数理学院宁德 352100;
2. 闽南师范大学数学与统计学院漳州 363000 Point-star Networks and Images of Metric Spaces Shou LIN¹, Yan Hui HUANG², Jing ZHANG²1. School of Mathematics and Physics, Ningde Normal University, Ningde 352100, P. R. China;
2. School of Mathematics and Statistics, Minnan Normal University Zhangzhou 363000, P. R. China

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摘要拓扑空间X的覆盖列{P_i}_i∈N被称为空间X的点星网，若x∈X，则{st（x，P_i）_i∈N是x在X中的网.本文刻画具有cs有限cs覆盖列的点星网的空间，并将其表示为度量空间在确定映射下的像.在假设集族性质P满足适当的条件下，证明对拓扑空间X下述条件相互等价:
（1）X具有P且cs覆盖列的点星网.
（2）X具有P且sn覆盖列的点星网.
（3）X是Cauchy sn对称空间且具有σ-P的cs网.
（4）X是Cauchy sn对称空间且具有σ-P的sn网.
（5）X是度量空间的序列覆盖、π且σ-P映像.
（6）X是度量空间的1序列覆盖、紧且σ-P映像.
这些工作以局部有限集族与点有限集族为特例，拓展了从基到cs网的研究，丰富了映射与空间的相互分类思想.

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收稿日期: 2019-01-21

MR (2010):

O189.1

基金资助:国家自然科学基金资助项目（11801254，11471153）

作者简介: 林寿,E-mail:shoulin60@163.com;黄燕晖,E-mail:645137233@qq.com;张静,E-mail:zhangjing86@126.com

引用本文:

林寿, 黄燕晖, 张静. 点星网与度量空间的映像[J]. 数学学报, 2019, 62(6): 865-878. Shou LIN, Yan Hui HUANG, Jing ZHANG. Point-star Networks and Images of Metric Spaces. Acta Mathematica Sinica, Chinese Series, 2019, 62(6): 865-878.

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