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.

引用

页码：2225 / 2233

页数：9

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