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2008 Construction of one-dimensional subsets of the reals not containing similar copies of given patterns
Tamás Keleti
Anal. PDE 1(1): 29-33 (2008). DOI: 10.2140/apde.2008.1.29

Abstract

For any countable collection of sets of three points we construct a compact subset of the real line with Hausdorff dimension 1 that contains no similar copy of any of the given triplets.

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Tamás Keleti. "Construction of one-dimensional subsets of the reals not containing similar copies of given patterns." Anal. PDE 1 (1) 29 - 33, 2008. https://doi.org/10.2140/apde.2008.1.29

Information

Received: 25 January 2008; Revised: 30 April 2008; Accepted: 30 May 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1151.28302
MathSciNet: MR2431353
Digital Object Identifier: 10.2140/apde.2008.1.29

Subjects:
Primary: 28A78

Keywords: affine copy , avoiding patterns , Erdös similarity problem , Hausdorff dimension , similar copy

Rights: Copyright © 2008 Mathematical Sciences Publishers

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