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On certain Glasner sets

Published online by Cambridge University Press:  12 July 2007

H. Kamarul Haili  and
R. Nair
H. Kamarul Haili
Affiliation:
School of Mathematical Sciences, University Science Malaysia, Minden 11800, Penang, Malaysia
R. Nair
Affiliation:
Mathematical Sciences, University of Liverpool, PO Box 147, Liverpool L69 7ZL, UK
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Abstract

A sequence of integers S is called Glasner if, given any ε > 0 and any infinite subset A of T = R/Z, and given y in T, we can find an integer n ∈ S such that there is an element of {nx : x ∈ A} whose distance to y is not greater than ε. In this paper we show that if a sequence of integers is uniformly distributed in the Bohr compactification of the integers, then it is also Glasner. The theorem is proved in a quantitative form.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 4 , August 2003 , pp. 849 - 853
Copyright
Copyright © Royal Society of Edinburgh 2003

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