一致结构与一致覆盖族的非标准刻画

The nonstardard characteristics of a uniformity and a collection of uniform covers

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.

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）.