On the Hausdorff dimension of ultrametric subsets in $\mathbb R^n$
Volume 218 / 2012
Fundamenta Mathematicae 218 (2012), 285-290
MSC: 30L05, 37F35.
DOI: 10.4064/fm218-3-5
Abstract
For every $\varepsilon>0$, any subset of $\mathbb{R}^n$ with Hausdorff dimension larger than $(1-\varepsilon)n$ must have ultrametric distortion larger than $1/(4\varepsilon)$.
