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Minimal bi-Lipschitz embedding dimension of ultrametric spaces

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Luukkainen J., Movahedi-Lankarani H.

Fundamenta Mathematicae

1994

tom 144

nr 2

181-193

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.