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A surprising covering of the real line
Author:
Gábor Kun
Journal:
Proc. Amer. Math. Soc. 134 (2006), 3555-3559
MSC (2000):
Primary 28A05, 03E15
Posted:
June 8, 2006
MathSciNet review:
2240667
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Abstract: We construct an increasing sequence of Borel subsets of  , such that their union is  , but  cannot be covered with countably many translations of one set. The proof uses a random method.
References
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M. Abért and T. Keleti, Shuffle the plane, Proc. Amer. Math. Soc. 130, (2002), 549-553. MR 1862136 (2003g:03070)
- 2.
Udayan B. Darji and Tamás Keleti, Covering
 with translates of a compact set, Proc. Amer. Math. Soc. 131 (2003), 2593-2596. MR 1974660 (2004d:03100)
- 3.
P. Erdos, Some remarks on set theory, Annals of Math. 44, (1943), 643-646.MR 0009614 (5:173c)
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Z. Ruzsa, Euklideszi terek fedése kis halmazokkal (in Hungarian), Thesis for the Master`s Degree (2001).
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P. Komjáth, Five degrees of separation, Proc. Amer. Math. Soc. 130, (2002), 2413-2417. MR 1897467 (2003c:03082)
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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
Posted:
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 after
28 years from publication.
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