2011/03/31 by Taras Banakh, Ihor Zarichnyi · 1 citation
Mathematics · #math.MG #math.GT #msc:54E35 #msc:54E40
published as Proc. of Intern. Geometry Center. Vol.3, No.4 (2010) 6-14 · 8 pages
arxiv created 2011/10/10 · arxiv updated 2011/10/11
We prove that each coarsely homogenous separable metric space X is coarsely equivalent to one of the spaces: the sigleton, the Cantor macro-cube or the Baire macro-space. This classification is derived from coarse characterizations of the Cantor macro-cube and of the Baire macro-space given in this paper. Namely, we prove that a separable metric space X is coarsely equivalent to the Baire macro-space if any only if X has asymptotic dimension zero and has unbounded geometry in the sense that for every δ there is ε such that no ε-ball in X can be covered by finitely many sets of diameter ≤ δ.