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A note on Gul’ko compact spaces. (English) Zbl 0622.54020

It is known that every Eberlein compact space has a dense \(G_{\delta}\) metrizable subset. We answer a question of M. Talagrand by showing that the same is true for the wider class of Gul’ko compact spaces. We also show that Gul’ko compact spaces satisfy a certain covering property hereditarily.

MSC:

54D30 Compactness
46B20 Geometry and structure of normed linear spaces
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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