2008/01/14 by Тарас Банах, Taras Banakh, Banakh, Taras +2 · 1 citation
Mathematics · #54E35 #54E40 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.GN #math.GT #msc:54E35 #msc:54E40
paper · pdf · doi:10.48550/arxiv.0801.2132
arxiv created 2008/01/14 · openalex publication_date 2008/01/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that two homogeneous ultra-metric spaces X,Y are coarsely equivalent if and only if Ent^\sharp(X)=Ent^\sharp(Y) where Ent^\sharp(X) is the so-called sharp entropy of X. This classification implies that each homogeneous proper ultra-metric space is coarsely equivalent to the anti-Cantor set 2<ω. For the proof of these results we develop a technique of towers which can have an independent interest.