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

 

Covering $\mathbb R$ with translates of a compact set


Authors: Udayan B. Darji and Tamás Keleti
Journal: Proc. Amer. Math. Soc. 131 (2003), 2593-2596
MSC (1991): Primary 03E15; Secondary 28A78
Published electronically: November 14, 2002
MathSciNet review: 1974660
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Abstract | References | Similar Articles | Additional Information

Abstract: Motivated by a question of Gruenhage, we investigate when $\mathbb R$is the union of less than continuum many translates of a compact set $C \subseteq\mathbb R$. It will follow from one of our general results that if a compact set $C$ has packing dimension less than 1, then $\mathbb R$ is not the union of less than continuum many translates of $C$.


References [Enhancements On Off] (What's this?)

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Additional Information

Udayan B. Darji
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email: ubdarj01@athena.louisville.edu

Tamás Keleti
Affiliation: Department of Analysis Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
Email: elek@cs.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06773-4
PII: S 0002-9939(02)06773-4
Received by editor(s): January 24, 2002
Received by editor(s) in revised form: March 14, 2002
Published electronically: November 14, 2002
Additional Notes: The first author thanks the Fulbright Foundation and the Department of Analysis of Eötvös Loránd University for their hospitality
The second author was supported by OTKA grant F 029768
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society