A Hurewicz theorem for the Assouad-Nagata dimension

N. Brodskiy; J. Dydak; M. Levin; A. Mitra

doi:10.1112/jlms/jdn005

A Hurewicz theorem for the Assouad-Nagata dimension

N. Brodskiy, J. Dydak, M. Levin, A. Mitra

Department of Mathematics

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35 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	741-756
Number of pages	16
Journal	Journal of the London Mathematical Society
Volume	77
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jdn005
State	Published - 1 Jan 2008

ASJC Scopus subject areas

General Mathematics

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abstract = "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.",

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N2 - 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.

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A Hurewicz theorem for the Assouad-Nagata dimension

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