紧一致空间中函数的逼近定理

The Approximation Theorem in Compact Uniform Space

一致空间作为一种特殊的拓扑空间,它与拓扑空间和度量空间存在着密切的联系.通过利用非标准分析的方法对紧一致空间进行了非标准刻画,得到了紧一致空间中函数收敛与连续之间的关系;同时,利用U-微连续的定义证明了一致空间上函数的逼近定理.

As a special topological space, uniform space has close contact with topological space and metric space. In this paper, the compact uniform space is nonstandard characterized by the methods of nonstandard analysis. The relationship between Convergent and continuity of func- tion are obtained; And the approximation theorem of function in uniform space are proved by the concept of U-microcontinuity.