Assouad-Nagata dimension via Lipschitz extensions
Assouad-Nagata dimension via Lipschitz extensions
复制标题
通过 Lipschitz 扩展的 Assouad-Nagata 维度
DOI：
10.1007/s11856-009-0056-3
复制
发表时间：
2009
影响因子：
1
通讯作者：
A. Mitra
中科院分区：
文献类型：
--
作者：
N. Brodskiy;J. Dydak;J. Higes;A. Mitra
在本文的第一部分，我们展示了如何将几个维度理论(具有Higson性质的渐近维度、Gromov的渐近维度和Buyalo[7]的容量维度)与AsSouad-Nagata维度联系起来。这是通过在度量空间的Lipschitz范畴上应用两个函子来完成的：微观和宏观。在第二部分中，我们将(在有限的Assuad-Nagata维空间中)至多n维的AsSouad-Nagata维空间确定为n球面S_n是Lipschitz扩张子的空间。给出了该结果的大规模和小规模模拟结果。
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 [7]) to Assouad-Nagata 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 Assouad-Nagata dimension) spaces of Assouad-Nagata dimension at most n as those for which the n-sphere Sn is a Lipschitz extensor. Large scale and small scale analogues of that result are given.