Vol. 1, No. 1, 2008
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Construction of one-dimensional subsets of the reals not containing similar copies of given patterns

Tamás Keleti
Vol. 1 (2008), No. 1, 29–33
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.

Keywords
Hausdorff dimension, avoiding patterns, Erdös similarity problem, similar copy, affine copy
Mathematical Subject Classification 2000
Primary: 28A78
Milestones
Received: 25 January 2008
Revised: 30 April 2008
Accepted: 30 May 2008
Published: 2 October 2008
Authors
Tamás Keleti
Department of Analysis
Eötvös Loránd University
Pázmány Péter sétány 1/C
H-1117 Budapest
Hungary
http://www.cs.elte.hu/analysis/keleti