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A Hurewicz theorem for the Assouad–Nagata dimension
Author(s) -
Brodskiy N.,
Dydak J.,
Levin M.,
Mitra A.
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn005
Subject(s) - mathematics
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.