A coarse characterization of the Baire macro-space

Details A coarse characterization of the Baire macro-space A coarse characterization of the Baire macro-space

2011-03-26

arxiv.org/abs/1103.5118v2

Proc. of Intern. Geometry Center. Vol.3, No.4 (2010) 6-14

Mathematics

Metric Geometry

8 pages

Scientific paper

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 $\delta$ there is $\epsilon$ such that no $\epsilon$-ball in $X$ can be covered by finitely many sets of diameter $\le \delta$.

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