| 拓扑空间可度量化的充要条件 |
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| 引用本文： | 陈娟,高随祥.拓扑空间可度量化的充要条件[J].数学杂志,2015,35(4):952-956. |
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| 作者姓名： | 陈娟 高随祥 |
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| 作者单位： | 中国科学院大学数学科学学院, 北京 101408,中国科学院大学数学科学学院, 北京 101408 |
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| 基金项目： | 国家重点基础研究发展计划(973)项目基金资助(2011CB706901);国家自然科学基金项目基金资助(11331012). |
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| 摘 要： | 本文研究了拓扑空间的可度量化的充要条件.利用可数开覆盖的性质和度量化的遗传性及定义,获得了拓扑空间可度量化的两个充要条件结果,推广了构造可度量化的拓扑空间和判断拓扑空间是度量空间的依据.
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| 关 键 词： | 拓扑空间 度量空间 可度量化 充要条件 |
| 收稿时间： | 2013/11/14 0:00:00 |
| 修稿时间： | 2014/5/19 0:00:00 |
THE NECESSARY AND SUFFICIENT CONDITION OF TOPOLOGICAL SPACE BEING METRIZABLE |
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| CHEN Juan and GAO Sui-xiang.THE NECESSARY AND SUFFICIENT CONDITION OF TOPOLOGICAL SPACE BEING METRIZABLE[J].Journal of Mathematics,2015,35(4):952-956. |
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| Authors: | CHEN Juan and GAO Sui-xiang |
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| Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China |
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| Abstract: | In this paper,we study the necessary and sufficient condition that a topological space is metrizable.By using the properties of countable open cover and metric space''s hereditary and definition,we give two necessary and sufficient conditions that a topological space is metrizable,which promote the foundation of structuring metrizable space and determining whether a topological space is metrizable. |
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| Keywords: | topological space metric space metrizable necessary and sufficient condition |
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