Uniform perfectness of self-affine sets

Authors:
Feng Xie, Yongcheng Yin and Yeshun Sun

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3053-3057

MSC (2000):
Primary 28A78, 28A80

Published electronically:
April 30, 2003

MathSciNet review:
1993212

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be affine maps of Euclidean space with each nonsingular and each contractive. We prove that the self-affine set of is uniformly perfect if it is not a singleton.

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Additional Information

**Feng Xie**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China

Address at time of publication:
420 Temple St., #517, New Haven, Connecticut 06511

Email:
xiefengmath@hotmail.com, feng.xie@yale.edu

**Yongcheng Yin**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China – and – Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China

Email:
yin@math.zju.edu.cn

**Yeshun Sun**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China

Email:
sun@math.zju.edu.cn

DOI:
http://dx.doi.org/10.1090/S0002-9939-03-06976-4

Keywords:
Uniformly perfect set,
self-affine set,
Hausdorff dimension

Received by editor(s):
February 24, 2002

Published electronically:
April 30, 2003

Additional Notes:
This research was supported by the National Natural Science Foundation of China, Project No. 10171090.

Communicated by:
Michael Handel

Article copyright:
© Copyright 2003
American Mathematical Society