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On the closure of a class of subsets of the real line

Published online by Cambridge University Press:  24 October 2008

I. Calvert
I. Calvert
Affiliation:
Department of Mathematics, Royal Holloway College, Englefield Green, Egham, Surrey
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Extract

A subset, X, of R belongs to the family T(a) if |X| ≥ 2 and, for all x and y belonging to X, ax + (1 − a) y ∈ X, where a ∈ R.

I consider the problem of determining for which values of a > 1 all elements of T(a) are dense in R.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 2 , March 1978 , pp. 181 - 182
Copyright
Copyright © Cambridge Philosophical Society 1978

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