On the open set condition for self-similar fractals
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- by Christoph Bandt, Nguyen Viet Hung and Hui Rao PDF
- Proc. Amer. Math. Soc. 134 (2006), 1369-1374 Request permission
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.References
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Additional Information
- Christoph Bandt
- Affiliation: Institute for Mathematics, Arndt University, 17487 Greifswald, Germany
- MR Author ID: 30465
- 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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1369-1374
- MSC (2000): Primary 28A80; Secondary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-05-08300-0
- MathSciNet review: 2199182