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\(P\)-filters and hereditary Baire function spaces. (English) Zbl 0969.54016

Summary: We extend the results of S. P. Gul’ko and G. A. Sokolov [ibid. 85, No. 1-3, 137-142 (1998; Zbl 0919.54011)] proving that a filter \(F\) on \(\omega\), regarded as a subspace of the Cantor set \(2^\omega\), is a hereditary Baire space if and only if \(F\) is a nonmeager (i.e., second category) \(P\)-filter. We also prove related results on hereditary Baire spaces of continuous functions \(C_p(X)\).

MSC:

54C35 Function spaces in general topology
54E52 Baire category, Baire spaces
03E05 Other combinatorial set theory

Citations:

Zbl 0919.54011
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References:

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