There is no universal proper metric spaces for asymptotic dimension 1

2022/11/19 by Mykhailo Zarichnyi, Zarichnyi, Mykhailo
Mathematics · #54E35 #54F45 #Algebraic Geometry and Number Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2211.10761

openalex publication_date 2022/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Answering a question of Ma, Siegert, and Dydak we show that there is no universal proper metric space for the asymptotic dimension n≥1.

Related

• Universal spaces for asymptotic dimension
• Universal spaces for asymptotic dimension zero
• Remarks on asymptotic power dimension
• On transfinite extension of asymptotic dimension
• Metric spaces with subexponential asymptotic dimension growth