Nagata-Assouad dimension via Lipschitz extensions

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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 \cite{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 $S^n$ is a Lipschitz extensor. Large scale and small scale analogs of that result are given.

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Metric Geometry, Geometric Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/107478

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601226
 http://arxiv.org/abs/math/0601226

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arXiv