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The Thickness And Quasisymmetrical Equivalence Of The Sets Defined By Digit Restrictions

Author

Listed:
  • YUXIA DAI

    (Department of Mathematics and Statistics, Hubei University, Wuhan 430062, P. R. China)

  • HAOTIAN QIN

    (Department of Mathematics and Statistics, Hubei University, Wuhan 430062, P. R. China)

  • SHANGYU WANG

    (School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, P. R. China)

  • CHUN WEI

    (School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, P. R. China)

Abstract

In this paper, we discuss the thickness and quasisymmetric equivalence of a class of fractal sets based on the binary expansion of numbers. We give the sufficient and necessary conditions for the thickness of this kind of sets to be positive, and the necessary and sufficient condition for their quasisymmetric equivalence with the standard Cantor ternary set. This paper also studies the relationship between the thickness and the uniform completeness about the product sets of two sets defined by digit restrictions.

Suggested Citation

  • Yuxia Dai & Haotian Qin & Shangyu Wang & Chun Wei, 2023. "The Thickness And Quasisymmetrical Equivalence Of The Sets Defined By Digit Restrictions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-7.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:05:n:s0218348x23500512
    DOI: 10.1142/S0218348X23500512
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