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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:

54E20 Stratifiable spaces, cosmic spaces, etc.
54E30 Moore spaces
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