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Remarks about a transitive version of perfectly meager sets. (English) Zbl 0879.03014

Summary: We show that if \(X\) has the property that every continuous image into Baire space is bounded and \(2^{\omega}\) is not a continuous image of \(X\), then \(X\) is always of first category in some additive sense. This gives an answer to an oral question of L. Bukovský, whether every wQN set has the latter property.

MSC:

03E05 Other combinatorial set theory
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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