A surprising covering of the real line
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- by Gábor Kun PDF
- Proc. Amer. Math. Soc. 134 (2006), 3555-3559 Request permission
Abstract:
We construct an increasing sequence of Borel subsets of $\mathbb {R}$, such that their union is $\mathbb {R}$, but $\mathbb {R}$ cannot be covered with countably many translations of one set. The proof uses a random method.References
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Additional Information
- Gábor Kun
- Affiliation: Department of Algebra and Number Theory, Eötvös Loránd University, 1117 Pázmány Péter sétány 1/c, Budapest, Hungary
- Email: kungabor@cs.elte.hu
- Received by editor(s): September 23, 2003
- Received by editor(s) in revised form: November 10, 2004, and June 17, 2005
- Published electronically: June 8, 2006
- Additional Notes: The research of the author was supported by OTKA grant no. T032042 and T049786. The author is indebted to Z. Ruzsa for his helpful remarks.
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3555-3559
- MSC (2000): Primary 28A05, 03E15
- DOI: https://doi.org/10.1090/S0002-9939-06-08371-7
- MathSciNet review: 2240667