, Volume 26, Issue 2, pp 561-571

Asymptotic dimension, property A, and Lipschitz maps

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Abstract

It is well-known that a paracompact space X is of covering dimension n if and only if any map f:XK from X to a simplicial complex K can be pushed into its n-skeleton K (n). We use the same idea to define dimension in the coarse category. It turns out the analog of maps f:XK is related to asymptotically Lipschitz maps, the analog of paracompact spaces are spaces related to Yu’s Property A, and the dimension coincides with Gromov’s asymptotic dimension.