关键词: CSS空间, 拟G_δ(2) 对角线, g 函数,  β 空间

Abstract:

A space X is a CSS space if  compact sets are uniformly G_δ sets. In the first part of this note, the authors mainly prove that, if a space X has a quasi-G_δ (2) diagonal, then X is a CSS space. They also show that the  countable product of CSS spaces is a CSS space, and if $X$ is the union of a family of countable closed CSS subspaces, then X is a CSS space. In the second part, the authors mainly show that, if X is the union of a family of countable closed β-subspaces (semi-stratifiable spaces), then X is a β-space (semi-stratifiable space).

Key words: CSS space, Quasi-G_δ(2) diagonal, g function,  β-space