A Hurewicz theorem for the Assouad-Nagata dimension

被引：37

作者：

Brodskiy, N. ^{[1
]}

Dydak, J. ^{[1
]}

Levin, M. ^{[2
]}

Mitra, A. ^{[1
]}

机构：

[1] Univ Tennessee, Knoxville, TN 37996 USA

[2] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2008年 / 77卷

关键词：

D O I：

10.1112/jlms/jdn005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a function f : X -> Y of metric spaces, the classical Hurewicz theorem states that dim(X) <= dim(f) + dim(Y). We provide analogs of this theorem for the Assouad-Nagata dimension, asymptotic Assouad-Nagata dimension, and asymptotic dimension (the latter result generalizes a theorem of Bell and Dranishnikov). As an application, we estimate the asymptotic Assouad-Nagata dimension of a finitely generated group G in terms of the asymptotic Assouad-Nagata dimensions of the groups K and H from the exact sequence 1 -> K -> G -> H -> 1.

引用

页码：741 / 756

页数：16

共 10 条

[1]

[Anonymous], 1993, GEOMETRIC GROUP THEO

[2] A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory [J].