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arXiv · 0909.4095

Asymptotic dimension, Property A, and Lipschitz maps

M. Cencelj·J. Dydak·A. Vavpetic
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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 from X to a simplicial complex K can be pushed into its n-skeleton. We use the same idea to define dimension in the coarse category. It turns out the analog of maps f from X to K 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.

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M. Cencelj, J. Dydak, A. Vavpetic. 2009-09-22. Asymptotic dimension, Property A, and Lipschitz maps. https://doi.org/10.1007/s13163-012-0102-2

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