## Real Analysis Exchange

### Remarks about a transitive version of perfectly meager sets

Andrzej Nowik

#### Abstract

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.

#### Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 406-412.

Dates
First available in Project Euclid: 1 June 2012

https://projecteuclid.org/euclid.rae/1338515234

Mathematical Reviews number (MathSciNet)
MR1433627

Zentralblatt MATH identifier
0879.03014

#### Citation

Nowik, Andrzej. Remarks about a transitive version of perfectly meager sets. Real Anal. Exchange 22 (1996), no. 1, 406--412. https://projecteuclid.org/euclid.rae/1338515234

#### References

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• W. Just, A. Miller, M. Scheepers and P. J. Szeptycki, The combinatorics of open covers (II), Topology and its Applications (to appear).
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• I. Recław, A note on QN-sets and wQN-sets, preprint, 1996.
• M. Scheepers, Additive properties of sets of real numbers and an infinite game, Quaestiones Mathematicae, 16 (1993), 177–191.