Universal spaces for asymptotic dimension zero

TL;DR

This paper constructs universal spaces for separable and proper metric spaces with asymptotic dimension zero, offering an alternative proof to a known result in the coarse category.

Contribution

It extends the construction of universal spaces for asymptotic dimension zero to separable and proper metric spaces, providing new methods and an alternative proof.

Findings

Constructed universal spaces for separable and proper metric spaces of asymptotic dimension zero

Provided an alternative proof to Dranishnikov-Zarichnyi's universal space construction

Enhanced understanding of coarse category spaces with 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.