Ultrametric spaces bi-Lipschitz embeddable in $ℝ^n$

Volume 150 / 1996

Kerkko Luosto Fundamenta Mathematicae 150 (1996), 25-42 DOI: 10.4064/fm-150-1-25-42


It is proved that if an ultrametric space can be bi-Lipschitz embedded in $ℝ^n$, then its Assouad dimension is less than n. Together with a result of Luukkainen and Movahedi-Lankarani, where the converse was shown, this gives a characterization in terms of Assouad dimension of the ultrametric spaces which are bi-Lipschitz embeddable in $ℝ^n$.


  • Kerkko Luosto

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