引用本文: | 刘普寅.度量空间的非标准特征(I)[J].国防科技大学学报,1995,17(1):109-116.[点击复制] |
Liu Puyin.The Nonstandard Character of Metric Spaces[J].Journal of National University of Defense Technology,1995,17(1):109-116[点击复制] |
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度量空间的非标准特征(I) |
刘普寅 |
(国防科技大学 系统工程与数学系 湖南 长沙 410073)
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摘要: |
本文首先引进度量空间非标准包的定义,然后将讨论非标准包的许多性质。在此基础上,用非标准方法来刻划度量空间中的各种紧性。最后应用这些结果,将证明Arzela-Ascoli定理,并在较弱的条件下,得到 Banach 不动点定理。 |
关键词: 非标准包,预近标准点,预紧集,预紧算子,几乎紧集 |
DOI: |
投稿日期:1994-11-20 |
基金项目:国家自然科学基金和国防科技大学青年科研基金资助项目 |
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The Nonstandard Character of Metric Spaces |
Liu Puyin |
(Department of Systems Engineering and Mathematics)
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Abstract: |
In the paper,We first introduce the definition of the nonstandard hull of a metric space. Many properties of the nonstandard hull are obtained. After that,with the nonstandard method. We describe a few of compact properties in a metric space. Finally with these conclusions,Arzela-Ascoli theorem is proved,and Banach fixed pointed theorem is obtained under the weaker conditions. |
Keywords: Nonstandard hull,Pre-nearstandard point,pre-compact set Pre-com-pact operator,Almost-compact set |
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