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Strongly meager sets and their uniformly continuous images


Authors: Andrzej Nowik and Tomasz Weiss
Journal: Proc. Amer. Math. Soc. 129 (2001), 265-270
MSC (2000): Primary 03E15, 03E20, 28E15
DOI: https://doi.org/10.1090/S0002-9939-00-05499-X
Published electronically: July 27, 2000
MathSciNet review: 1694343
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Abstract | References | Similar Articles | Additional Information

Abstract:

We prove the following theorems:

(1) Suppose that $f:2^\omega\to 2^\omega$ is a continuous function and $X$ is a Sierpinski set. Then

(A)
for any strongly measure zero set $Y$, the image $f[X+Y]$ is an $s_0$-set,
(B)
$f[X]$ is a perfectly meager set in the transitive sense.

(2) Every strongly meager set is completely Ramsey null.


References [Enhancements On Off] (What's this?)

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Additional Information

Andrzej Nowik
Affiliation: Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80 – 952 Gdańsk, Poland
Email: matan@paula.univ.gda.pl

Tomasz Weiss
Affiliation: Institute of Mathematics, WSRP, 08-110 Siedlce, Poland
Email: weiss@wsrp.siedlce.pl

DOI: https://doi.org/10.1090/S0002-9939-00-05499-X
Keywords: Strongly meager set, always first category set
Received by editor(s): July 16, 1998
Received by editor(s) in revised form: September 9, 1998, and March 10, 1999
Published electronically: July 27, 2000
Additional Notes: The first author was partially supported by the KBN grant 2 P03A 047 09.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society

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