#### 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
##### 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
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