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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the boundaries of self-similar tiles in $\mathbb {R}^1$
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by Xing-Gang He PDF
Proc. Amer. Math. Soc. 134 (2006), 3163-3170 Request permission

Abstract:

The aim of this note is to study the construction of the boundary of a self-similar tile, which is generated by an iterated function system $\{\phi _i(x)=\frac {1}{N} (x+d_i)\}_{i=1}^N$. We will show that the boundary has complicated structure (no simple points) in general; however, it is a regular fractal set.
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Additional Information
  • Xing-Gang He
  • Affiliation: Department of Mathematics, Central China Normal University, Wuhan, 430079, People’s Republic of China
  • Email: xingganghe@sina.com
  • Received by editor(s): April 14, 2005
  • Published electronically: June 5, 2006
  • Additional Notes: This research was supported in part by SRF for ROCS(SEM)
  • Communicated by: Michael T. Lacey
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3163-3170
  • MSC (2000): Primary 28A80, 05B45
  • DOI: https://doi.org/10.1090/S0002-9939-06-08643-6
  • MathSciNet review: 2231899