Minimal bi-Lipschitz embedding dimension of ultrametric spaces

Volume 144 / 1994

Jouni Luukkainen , Hossein Movahedi-Lankarani Fundamenta Mathematicae 144 (1994), 181-193 DOI: 10.4064/fm-144-2-181-193

Abstract

We prove that an ultrametric space can be bi-Lipschitz embedded in $ℝ^n$ if its metric dimension in Assouad's sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.

Authors

  • Jouni Luukkainen Department of Mathematics
    P.O. Box 4 (Hallituskatu 15)
    FIN-00014 University of Helsinki
    Finland
    e-mail
  • Hossein Movahedi-LankaraniDepartment of Mathematics
    Penn State Altoona
    Altoona, PA 16601–3760
    U.S.A.
    e-mail

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