Universal spaces for asymptotic dimension zero

Abstract

Dranishnikov and Zarichnyi constructed a universal space in the coarse category of spaces of bounded geometry of asymptotic dimension $0$. In this paper we construct universal spaces in the coarse category of separable (respectively, proper) metric spaces of asymptotic dimension $0$. Our methods provide an alternative proof of Dranishnikov-Zarichnyi result.

9 pages Added a new section Ultrametric groups as universal spaces and corrected spelling of some of non-English names