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

 

A surprising covering of the real line


Author: Gábor Kun
Journal: Proc. Amer. Math. Soc. 134 (2006), 3555-3559
MSC (2000): Primary 28A05, 03E15
Published electronically: June 8, 2006
MathSciNet review: 2240667
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08371-7
PII: S 0002-9939(06)08371-7
Keywords: Borel set, translates, countable, covering
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.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.