Asymptotic cones and Assouad-Nagata dimension

被引：12
|
作者：
Dydak, J. [1 ]
Higes, J. [2 ]
机构：
[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA
[2] Univ Complutense Madrid, Dept Geometria & Topologia, Fac CC Matemat, E-28040 Madrid, Spain
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 06期
关键词：
Assouad-Nagata dimension; asymptotic dimension; asymptotic cones; covering dimension;
D O I：
10.1090/S0002-9939-08-09149-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the dimension of any asymptotic cone over a metric space (X,rho) does not exceed the asymptotic Assouad-Nagata dimension asdim(AN)(X) of X. This improves a result of Dranishnikov and Smith (2007), who showed dim(Y) <= asdim(AN)(X) for all separable subsets Y of special asymptotic cones Cone(omega)(X), where omega is an exponential ultrafilter on natural numbers. We also show that the Assouad-Nagata dimension of the discrete Heisenberg group equals its asymptotic dimension.
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页码：2225 / 2233
页数：9
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