Minimal bi-Lipschitz embedding dimension of ultrametric spaces
Volume 144 / 1994
Fundamenta Mathematicae 144 (1994), 181-193
DOI: 10.4064/fm-144-2-181-193
Abstract
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.
