Minimal bi-Lipschitz embedding dimension of ultrametric spaces

• Autorzy: Jouni Luukkainen , Hossein Movahedi-Lankarani
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54F45: Dimension theory
• 54E40: Special maps on metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 144
• Numer: 2
• Strony: 181-193

Daty

wydano

1994

otrzymano

1993-03-24

Twórcy

autor

Jouni Luukkainen

• Department of Mathematics, P.O. Box 4 (hallituS.A.u 15), Fin-00014 University of Helsinki, Finland

autor

Hossein Movahedi-Lankarani

• epartment of Mathematics, Penn State Altoona, Altoona, Pa 16601-3760, U.S.A.

Bibliografia

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