Abstract
Gromov \cite{Gr} and Dranishnikov \cite{Dr} 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} and Dranishnikov-Keesling-Uspienskij \cite{DKU}.
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