| 箱积空间中的紧有限集族 |
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| 引用本文： | 林寿.箱积空间中的紧有限集族[J].数学年刊A辑(中文版),2017,38(3):269-276. |
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| 作者姓名： | 林寿 |
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| 作者单位： | 闽南师范大学数学与统计学院, 福建,!漳州 363000; 宁德师范学院数学研究所，福建,!宁德 352100. |
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| 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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| 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.
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| 关 键 词： | Box products Compact-finite families Subproper mappings $k^*$-metrizable spaces $k$-networks |
| 收稿时间： | 2015/6/7 0:00:00 |
| 修稿时间： | 2016/1/2 0:00:00 |
The Compact-Finite Families in Box Products |
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| LIN Shou.The Compact-Finite Families in Box Products[J].Chinese Annals of Mathematics,2017,38(3):269-276. |
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| Authors: | LIN Shou |
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| Institution: | School of Mathematics and Statistics, Minnan NormalUniversity, Zhangzhou 363000, Fujian, China. Institute ofMathematics, Ningde Normal University, Ningde 352100, Fujian, China. |
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| Abstract: | 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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| Keywords: | Box products Compact-finite families Subproper mappings $k^*$-metrizable spaces $k$-networks |
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