Nagata-Assouad dimension via Lipschitz extensions
度量几何
2007-05-23 v1 几何拓扑
摘要
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 as those for which the -sphere is a Lipschitz extensor. Large scale and small scale analogs of that result are given.
引用
@article{arxiv.math/0601226,
title = {Nagata-Assouad dimension via Lipschitz extensions},
author = {N. Brodskiy and J. Dydak and J. Higes and A. Mitra},
journal= {arXiv preprint arXiv:math/0601226},
year = {2007}
}