Ultrametric spaces bi-Lipschitz embeddable in $ℝ^n$
Volume 150 / 1996
Fundamenta Mathematicae 150 (1996), 25-42
DOI: 10.4064/fm-150-1-25-42
Abstract
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 $ℝ^n$.
