Universally meager sets
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Abstract:
We study category counterparts of the notion of a universal measure zero set of reals. We say that a set $A\subseteq {\mathbb R}$ is universally meager if every Borel isomorphic image of $A$ is meager in ${\mathbb R}$. We give various equivalent definitions emphasizing analogies with the universally null sets of reals. In particular, two problems emerging from an earlier work of Grzegorek are solved.References
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Additional Information
- Piotr Zakrzewski
- Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
- MR Author ID: 239503
- Email: piotrzak@mimuw.edu.pl
- Received by editor(s): March 23, 1999
- Received by editor(s) in revised form: September 7, 1999
- Published electronically: November 2, 2000
- Additional Notes: The author was partially supported by KBN grant 2 P03A 047 09 and by the Alexander von Humboldt Foundation.
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1793-1798
- MSC (1991): Primary 03E20, 54E52; Secondary 54G99, 28A05
- DOI: https://doi.org/10.1090/S0002-9939-00-05726-9
- MathSciNet review: 1814112