Covering $\mathbb R$ with translates of a compact set
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- by Udayan B. Darji and Tamás Keleti PDF
- Proc. Amer. Math. Soc. 131 (2003), 2593-2596 Request permission
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
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Additional Information
- Udayan B. Darji
- Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
- MR Author ID: 318780
- ORCID: 0000-0002-2899-919X
- Email: ubdarj01@athena.louisville.edu
- Tamás Keleti
- Affiliation: Department of Analysis Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
- MR Author ID: 288479
- Email: elek@cs.elte.hu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2593-2596
- MSC (1991): Primary 03E15; Secondary 28A78
- DOI: https://doi.org/10.1090/S0002-9939-02-06773-4
- MathSciNet review: 1974660