| 抽象度量空间的拓扑结构 |
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| 引用本文： | 郑权.抽象度量空间的拓扑结构[J].华中科技大学学报(自然科学版),1990(6). |
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| 作者姓名： | 郑权 |
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| 作者单位： | 华中理工大学数学系 |
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| 摘 要： | 本文给半序空间设置了一套合理的公理系统,对其上取值的抽象度量空间引入拓扑结构。证明了抽象度量空间中点列的收敛性与同一点列在所引入拓扑下的收敛性是一致的,并在隔离性、可分性及紧性方面得到与通常度量空间中相似的结果。
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| 关 键 词： | 拓扑结构 度量空间 半序空间 隔离性 可分性 紧性 |
The Topological Structure of Abstract Metric Space |
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| Zheng Quan.The Topological Structure of Abstract Metric Space[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,1990(6). |
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| Authors: | Zheng Quan |
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| Abstract: | A perfect axiom system for semi-order space is proposed. With a standard method one can introduce a topology Yr in the abstract metric space (X,r) with values in the above semi-order space. The main results obtained are as follows: (a) The convergence defined in (X,r) is equivalent to that in (X,Yr); (b) (X,Yr) is a T3 space; (c) (X,Yr) is separable if and only if it is second countable, or a Lindeloef space; (d) The compactness in X is equivalent to the sequential compactness in X. |
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| Keywords: | Topological structure Metric space Semi-order space Separation property Separability Compactness |
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