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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sierpiński sets and strong first category


Authors: Jakub Jasiński and Tomasz Weiss
Journal: Proc. Amer. Math. Soc. 111 (1991), 235-238
MSC: Primary 28A05; Secondary 04A15
MathSciNet review: 1039257
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Abstract: We prove that if $ S$ is a Sierpinski set and $ N \subseteq \mathbb{R}$ is an $ {F_\sigma }$ set of measure zero, then $ (N + t) \cap S = \emptyset $ for some $ t \in \mathbb{R}$. A similar result holds for generalized Sierpinski sets under Martin's Axiom.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1039257-X
PII: S 0002-9939(1991)1039257-X
Article copyright: © Copyright 1991 American Mathematical Society