Article

# A Hurewicz theorem for the Assouad-Nagata dimension

• ##### Michael Levin
06/2006; DOI: 10.1112/jlms/jdn005
Source: arXiv

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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