| 林寿.箱积空间中的紧有限集族[J].数学年刊A辑,2017,38(3):269~276 |
| 箱积空间中的紧有限集族 |
| The Compact-Finite Families in Box Products |
| Received:June 07, 2015 Revised:January 02, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0022 |
| 中文关键词: Box products, Compact-finite families, Subproper mappings, $k^*$-metrizable spaces, $k$-networks |
| 英文关键词:Box products, Compact-finite families, Subproper mappings, $k^*$-metrizable spaces, $k$-networks |
| 基金项目:本文受到国家自然科学基金(No.11471153)的资助. |
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| 中文摘要: |
| 箱积中正规性或仿紧性的研究是一般拓扑学中极其困难的问题.
作者以紧有限闭扩张和定理为基础, 建立了一个广义度量空间类的箱积定理,
由此导出$k^*$ 可度量空间及具有点可数$k$ 网的空间等均关于箱积运算保持. |
| 英文摘要: |
| The study on normality or paracompactness in box products is an extremely difficult question in general topology.
In this paper, a box product theorem on generalized metric spaces is established
by compact-finite sum theorems of closed expansions.
It follows that $k^*$-metrizable spaces, spaces with point-countable $k$-networks are preserved by box products. |
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