Nagata-Assouad dimension via Lipschitz extensions
| dc.creator | Brodskiy, N. | |
| dc.creator | Dydak, J. | |
| dc.creator | Higes, J. | |
| dc.creator | Mitra, A. | |
| dc.date | 2006-01-10 | |
| dc.date.accessioned | 2026-07-07T06:58:44Z | |
| dc.date.available | 2026-07-07T06:58:44Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0601226 | |
| dc.identifier | http://arxiv.org/abs/math/0601226 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107478 | |
| dc.subject | Metric Geometry | |
| dc.subject | Geometric Topology | |
| dc.title | Nagata-Assouad dimension via Lipschitz extensions | |
| dc.type | text |