Self-similar sets with an open set condition and great variety of overlaps

Authors:
Christoph Bandt and Nguyen Viet Hung

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3895-3903

MSC (2000):
Primary 28A80; Secondary 37B10, 37F20

Published electronically:
May 22, 2008

MathSciNet review:
2425729

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a very simple family of self-similar sets with two pieces, we prove, using a technique of Solomyak, that the intersection of the pieces can be a Cantor set with any dimension in as well as a finite set of any cardinality . The main point is that the open set condition is fulfilled for all these examples.

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Additional Information

**Christoph Bandt**

Affiliation:
Institute for Mathematics and Informatics, Arndt University, 17487 Greifswald, Germany

Email:
bandt@uni-greifswald.de

**Nguyen Viet Hung**

Affiliation:
Department of Mathematics, Hue University, Hue, Vietnam

Email:
nvh0@yahoo.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09349-0

Received by editor(s):
March 16, 2007

Received by editor(s) in revised form:
September 19, 2007

Published electronically:
May 22, 2008

Communicated by:
Jane M. Hawkins

Article copyright:
© Copyright 2008
By the authors