| 一致结构与一致覆盖族的非标准刻画 |
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| 引用本文： | 陈东立,宋昊,史艳维. 一致结构与一致覆盖族的非标准刻画[J]. 纯粹数学与应用数学, 2011, 27(3): 292-296 |
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| 作者姓名： | 陈东立 宋昊 史艳维 |
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| 作者单位： | 1. 西安建筑科技大学理学院,陕西西安,710055
2. 西安培华学院基础部,陕西西安,710125 |
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| 基金项目： | 陕西省自然科学基金，西安培华学院校级课题项目 |
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| 摘 要： | 一致空间有三种等价描述方式,即通过满足各自条件的关系族,覆盖族和伪度量族.本文利用非标准分析的方法研究了一致空间,给出了一致结构与一致覆盖族的非标准刻画,并且利用（X×X）上的可滤单子化的等价关系构造了X上的一致结构.
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| 关 键 词： | 单子 可滤单子化 ＊-加细 一致覆盖族 |
The nonstardard characteristics of a uniformity and a collection of uniform covers |
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| CHEN Dong-li,SONG Hao,SHI Yan-wei. The nonstardard characteristics of a uniformity and a collection of uniform covers[J]. Pure and Applied Mathematics, 2011, 27(3): 292-296 |
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| Authors: | CHEN Dong-li SONG Hao SHI Yan-wei |
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| Affiliation: | 1.School of Science,Xi’an University of Architecture and Technology,Xi’an 710055,China;2.Department of Basic Courses,Xi’an Peihua University,Xi’an 710125,China) |
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| Abstract: | The concept of uniformity may be described in three equivalent ways: as a collection of relations,as a collection of covers of X,as a collection of pseudometrics,where each of these collections satisfies a respective condition.In this paper,the uniform spaces are studied by nonstandard analsys,and characterizes of a uniformity and a collection of uniform covers are gained.It constructs a uniformity on X by used of an equivalence relation which is filter-monadic in *(X × X). |
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| Keywords: | monad filter-monadic *-refines collection of uniform covers |
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