局部可分度量空间的闭S映象

Closed S Images of Locally Separable Metric Spaces

给出局部可分度量空间闭S映象的一些内部刻划 ,证明了空间X是局部可分度量空间的闭S映象 ,当且仅当X是Fr啨ｃｈｅｔ空间且具有由可分子空间组成的σ 局部有限k 网 ,当且仅当X具有由可分子空间组成的σ 局部有限Fr啨ｃｈｅｔ拟基。

In this paper, we have given an intemal depiction of closed S images of locally separable metric spaces.We have shown that space X is a closed S image of a locally separable metric space if and only if X is a Fréchet space which has a σ locally finite k net made of separable subspaces, and if and only if X has a σ locally finite Fréchet quasi base made of separable subspaces.