Sierpiński sets and strong first category
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- by Jakub Jasiński and Tomasz Weiss
- Proc. Amer. Math. Soc. 111 (1991), 235-238
- DOI: https://doi.org/10.1090/S0002-9939-1991-1039257-X
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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.References
- Tomek Bartoszyński and Haim Judah, On Sierpiński sets, Proc. Amer. Math. Soc. 108 (1990), no. 2, 507–512. MR 991689, DOI 10.1090/S0002-9939-1990-0991689-0
- P. Erdős, K. Kunen, and R. Daniel Mauldin, Some additive properties of sets of real numbers, Fund. Math. 113 (1981), no. 3, 187–199. MR 641304, DOI 10.4064/fm-113-3-187-199
- Arnold W. Miller, Special subsets of the real line, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 201–233. MR 776624
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 235-238
- MSC: Primary 28A05; Secondary 04A15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1039257-X
- MathSciNet review: 1039257