Universally meager sets
Author:
Piotr Zakrzewski
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
Published electronically:
November 2, 2000
MathSciNet review:
1814112
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
We study category counterparts of the notion of a universal measure zero set of reals.
We say that a set 
is universally meager if every Borel isomorphic image of 
is meager in 
. 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.
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Additional Information
Piotr Zakrzewski
Affiliation:
Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
Email:
piotrzak@mimuw.edu.pl
DOI:
https://doi.org/10.1090/S0002-9939-00-05726-9
Keywords:
Measure and category,
Borel sets,
Baire property,
$\sigma$-algebra,
$\sigma$-ideal
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.
Article copyright:
© Copyright 2000
American Mathematical Society
