一致结构单子的应用

Monad of a Uniformity and Some Applications

一致空间作为一种特殊的拓扑空间,是连接度量空间与拓扑空间的重要桥梁,它将Cauchy序列、完备等概念由度量空间拓展到拓扑空间。文中利用非标准分析的方法证明了一致空间上Cauchy滤子与一致结构单子之间的关系,一致结构点单子的性质及Cauchy网与聚点之间存在的关系。

As a special kind of topological space,the uniform space is an important bridge between metric space and the topological space and expands the concepts of the Canchy sequence,completeness and so on from the metric space to the topological space. In this article,the relationship between the Cauchy filter and the monad of a uniformity the property about the point monad of a uniformity,the relationship between the Cauchy net and the cluster point on the uniform space are proved by utilizing the method of the nonstandard analysis.