|
| 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. |
| 关键词: 拓扑空间 度量空间 可度量化 充要条件 |
| DOI： |
| 分类号:O189.11 |
| 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). |
|
| THE NECESSARY AND SUFFICIENT CONDITION OF TOPOLOGICAL SPACE BEING METRIZABLE |
|
CHEN Juan,GAO Sui-xiang
|
| 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. |
| Key words: topological space metric space metrizable necessary and sufficient condition |
