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Title

Minimal bi-Lipschitz embedding dimension of ultrametric spaces

Authors 1, 2

Affiliations

  1. Department of Mathematics, P.O. Box 4 (hallituS.A.u 15), Fin-00014 University of Helsinki, Finland
  2. epartment of Mathematics, Penn State Altoona, Altoona, Pa 16601-3760, U.S.A.

Abstract

We prove that an ultrametric space can be bi-Lipschitz embedded in ℝn 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.

Bibliography

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm144/fm14426.pdf

Fundamenta Mathematicae
1994/144/2
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Pages:
181-193
Main language of publication
English
Received
1993-03-24
Published
1994
Exact and natural sciences