A coarse characterization of the Baire macro-space

Autor:	Banakh, Taras, Zarichnyi, Ihor
Rok vydání:	2011
Předmět:	Mathematics - Metric Geometry Mathematics - Geometric Topology 54E35 54E40
Zdroj:	Proc. of Intern. Geometry Center. Vol.3, No.4 (2010) 6-14
Druh dokumentu:	Working Paper
Popis:	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 $\le \delta$. Comment: 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1103.5118 Zobrazit plný text záznamu View this record from Arxiv