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.
"Remarks about a transitive version of perfectly meager sets." Real Anal. Exchange 22 (1) 406 - 412, 1996/1997.