Nagata-Assouad dimension via Lipschitz extensions
Brodskiy, N. · Dydak, J. · Higes, J. · Mitra, A.
Original · EN
In the first part of the paper we show how to relate several dimension theories (asymptotic dimension with Higson property, asymptotic dimension of Gromov, and capacity dimension of Buyalo Buyalo1) to Nagata-Assouad dimension. This is done by applying two functors on the Lipschitz category of metric spaces: microscopic and macroscopic. In the second part we identify (among spaces of finite Nagata-Assouad dimension) spaces of Nagata-Assouad dimension at most n as those for which the n-sphere Sⁿ is a Lipschitz extensor. Large scale and small scale analogs of that result are given.
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