Open Access
2000/2001 The Erdős Similarity Problem
R. E. Svetic
Real Anal. Exchange 26(2): 525-540 (2000/2001).


Erdős posed the following problem. "Let $E$ be an infinite set of real numbers. Prove that there is a set of real numbers $S$ of positive measure which does not contain a set $E^\prime$ similar (in the sense of elementary geometry) to $E$.'' The proof is known for only a few special cases; and not included among these is the geometric sequence $\{2^{-n}\}_{n=1}^\infty$. In this paper we examine the known literature, present some new results, and ask a few related questions.


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R. E. Svetic. "The Erdős Similarity Problem." Real Anal. Exchange 26 (2) 525 - 540, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 27 June 2008

zbMATH: 1014.28502
MathSciNet: MR1844133

Primary: 28A05
Secondary: 28A99

Keywords: Erd\H{o}s Set , Erd\H{o}s Similarity Problem , Property E , Universal Set

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 2 • 2000/2001
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