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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the open set condition for self-similar fractals


Authors: Christoph Bandt, Nguyen Viet Hung and Hui Rao
Journal: Proc. Amer. Math. Soc. 134 (2006), 1369-1374
MSC (2000): Primary 28A80; Secondary 28A75
Published electronically: October 6, 2005
MathSciNet review: 2199182
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Abstract: For self-similar sets, the existence of a feasible open set is a natural separation condition which expresses geometric as well as measure-theoretic properties. We give a constructive approach by defining a central open set and characterizing those points which do not belong to feasible open sets.


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Additional Information

Christoph Bandt
Affiliation: Institute for Mathematics, Arndt University, 17487 Greifswald, Germany
Email: bandt@uni-greifswald.de

Nguyen Viet Hung
Affiliation: Institute for Mathematics, Arndt University, 17487 Greifswald, Germany
Email: nvh0@yahoo.com

Hui Rao
Affiliation: Department of Mathematics, Tsinghua University, P.O. Box 100084, Beijing, People’s Republic of China
Email: HRao@math.tsinghua.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08300-0
PII: S 0002-9939(05)08300-0
Keywords: Self-similar, fractals, iterated function system
Received by editor(s): October 26, 2004
Received by editor(s) in revised form: December 2, 2004
Published electronically: October 6, 2005
Additional Notes: The third author was supported by the German Research Foundation (DFG), and the second author was supported by the Vietnamese Government and the German Academic Exchange Service (DAAD)
Communicated by: David Preiss
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.