| 引用本文: | 刘普寅.度量空间的非标准特性(Ⅱ).[J].国防科技大学学报,1995,17(4):124-131.[点击复制] |
| Liu Puyin.The Nonstandard Character of Metric Spaces(Ⅱ)[J].Journal of National University of Defense Technology,1995,17(4):124-131[点击复制] |
|
| |
|
|
| 本文已被：浏览 6211次 下载 869次 |
| 度量空间的非标准特性(Ⅱ) |
| 刘普寅 |
|
(国防科技大学 系统工程与数学系 湖南 长沙 410073)
|
| 摘要: |
| 本文在文《度重空间的非标准特性(Ⅰ)》的基础上，用非标准分析方法刻划了度量空间上的全有界映射与紧映射的许多特性，并给出了一个赋范线性空间的维数有限的非标准特征。最后，在赋范线性空间中，通过弱拓扑性质的非标准刻划，简洁地证明了Eber-lein-Ⅲмупвян定理。 |
| 关键词: 紧映射，全有界映射，w-预近标准点，w-紧点，w-近标准点 |
| DOI： |
| 投稿日期：1995-04-15 |
| 基金项目:国家自然科学基金资助项目 |
|
| The Nonstandard Character of Metric Spaces(Ⅱ) |
| Liu Puyin |
|
(Department of System Engineering and Mathematics)
|
| Abstract: |
| In the paper，we continue the research of [1]. With the nonstandard analytical method，many properties of the totally bounded mapping and the compact mapping are described in the metric space. The nonstandard character that a norm space is a finite dimension space is given. Finally，by the nonstandard description of the weak topological properties，Eberlein-Ⅲмупвян theorem is succinctly proved in the norm space. |
| Keywords: compact mapping,totally bounded mapping,w-prenearstandard point,w-compact point,w-nearstandard point |
|
|
