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Deformations on Symbolic Cantor Sets and Ultrametric Spaces

  • Qingshan Zhou
  • Xining Li
  • Yaxiang LiEmail author
Article
  • 4 Downloads

Abstract

By introducing new deformations on symbolic Cantor sets and ultrametric spaces, we prove that doubling ultrametric spaces admit bilipschitz embedding into Cantor sets. If in addition the spaces are uniformly perfect, we show that they are quasisymmetrically equivalent to Cantor sets. Moreover, we provide a new proof for a recent work of Heer regarding quasimöbius uniformization of Cantor set.

Keywords

Symbolic Cantor set Ultrametric space Bilipschitz map Quasisymmetric map Quasimöbius map 

Mathematics Subject Classification

Primary: 30C65 30F45 Secondary: 30C20 

Notes

Acknowledgements

The authors are indebted to the referee for the valuable suggestions.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.School of Mathematics and Big DataFoshan UniversityFoshanPeople’s Republic of China
  2. 2.Department of MathematicsSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  3. 3.School of Mathematics (Zhuhai)Sun Yat-sen UniversityZhuhaiPeople’s Republic of China
  4. 4.Department of MathematicsHunan First Normal UniversityChangshaPeople’s Republic of China

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