# A metric characterization of snowflakes of Euclidean spaces

created by ledonne on 25 Aug 2014

[BibTeX]

Preprint

Inserted: 25 aug 2014
Last Updated: 25 aug 2014

Year: 2014

Abstract:

We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to $\mathbb R^n$ equipped with a distance $(d_{\rm E})^\epsilon$, for some $n\in \mathbb N_0$ and $\epsilon\in (0,1]$, where $d_{\rm E}$ is the Euclidean distance, if and only if it is locally compact, $2$-point isometrically homogeneous, and admits dilations of any factor.