Coarse dimensions and partitions of unity

Details Coarse dimensions and partitions of unity Coarse dimensions and partitions of unity

2005-06-27

arxiv.org/abs/math/0506547v3

Rev. R. Acad. Cien. Serie A. Mat. 102 (1), 2008, pp. 1-19

Mathematics

Geometric Topology

23 pages

Scientific paper

Gromov \cite{Gr$_1$} and Dranishnikov \cite{Dr$_1$} introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov \cite{Dr$_1$} and Dranishnikov-Keesling-Uspienskij \cite{DKU}.

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