Proceedings of the American Mathematical Society

Author(s): Tomasz Szarek; Stanislaw Wedrychowicz
Journal: Proc. Amer. Math. Soc. 133 (2005), 437-440.
MSC (2000): Primary 28A80; Secondary 28A78
Posted: September 2, 2004
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Abstract: It is shown that every class of contracting similitudes $\{f_{1},\ldots , f_{N}\}$ on $R^{s}$ satisfying the OSC and such that $\dim _{H} \mathcal{K}_{0}<s$ , where $\mathcal{K}_{0}$ denotes the corresponding fractal, can be extended to an infinite family of contracting similitudes which still satisfies the OSC but the SOSC does not hold.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 28A80, 28A78

Tomasz Szarek
Affiliation: Institute of Mathematics, Silesian University -- and -- Institute of Mathematics of the Polish Academy of Sciences, Bankowa 14, 40--007 Katowice, Poland
Email: szarek@ux2.math.us.edu.pl

Stanislaw Wedrychowicz
Affiliation: Department of Mathematics, Technical University of Rzeszów, W. Pola 6, 35--959 Rzeszów, Poland

DOI: 10.1090/S0002-9939-04-07708-1
PII: S 0002-9939(04)07708-1
Keywords: Fractal, open set condition, strong open set condition
Received by editor(s): July 2, 2003
Posted: September 2, 2004
Additional Notes: The first author's research was supported by the State Committee for Scientific Research Grant No. Z PO3A 031 25
Communicated by: Michael Handel
Copyright of article: Copyright 2004, American Mathematical Society

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