局部可分度量空间闭s映象的注记

A Note on Closed s-images of Locally Separable Metric Spaces

该文讨论局部可分度量空间闭s映象的分解定理,证明了正则的Frechet空间是局部可分度量空间的闭s映象当且仅当满足如下条件:具有点可数的cs网,第一可数的闭子空间是局部可分的,且Lindelf的闭子空间是可分的．

In this note a decomposition theorem about closed s-images of locally separable metric spaces is discussed. It is showed that a regular Frechet space is a closed s-image of a locally separable metric space if and only if it has a point-countable cs^＊-network, each first countable closed subset is locally separable, and each LindelSf closed subset is separable.