## On CSS spaces and related conclusions.(Chinese. English summary)Zbl 1224.54065

Summary: A space $$X$$ is a CSS space if compact sets are uniformly $$G_\delta$$ sets. In the first part of this note, the authors mainly prove that, if a space $$X$$ has a quasi-$$G_\delta(2)$$ 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 $$\beta$$-subspaces (semi-stratifiable spaces), then $$X$$ is a $$\beta$$-space (semi-stratifiable space).

### MSC:

 5.4e+21 Stratifiable spaces, cosmic spaces, etc. 5.4e+31 Moore spaces