Universal spaces for asymptotic dimension zero

2021/10/17 by Yuankui Ma, Ma, Yuankui, Jeremy Siegert +3
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Metric Geometry (math.MG) #Primary 54D35 #Secondary 20F69

paper · pdf · doi:10.48550/arxiv.2110.08929

openalex publication_date 2021/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Universal spaces for asymptotic dimension
• There is no universal proper metric spaces for asymptotic dimension 1
• Coarse structure of ultrametric spaces with applications
• Classification of metric spaces with infinite asymptotic dimension
• Relating asymptotic dimension to Ponomarev's cofinal dimension via coarse proximities