A Hurewicz theorem for the Assouad-Nagata dimension

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

Research output: Contribution to journalArticlepeer-review

23 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 languageEnglish
Pages (from-to)741-756
Number of pages16
JournalJournal of the London Mathematical Society
Volume77
Issue number3
DOIs
StatePublished - 1 Jan 2008

ASJC Scopus subject areas

  • Mathematics (all)

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