| 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 |
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(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 |
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(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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