A Hurewicz theorem for the Assouad�Nagata dimension

• Autores: Nikolay Brodskiy, Jerzy Dydak , Michael Levin, Atish Mitra
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 3, 2008, págs. 741-756
• Idioma: inglés
• DOI: 10.1112/jlms/jdn005
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• Resumen

  • 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.