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Journal of the London Mathematical Society Advance Access originally published online on March 14, 2008
Journal of the London Mathematical Society 2008 77(3):741-756; doi:10.1112/jlms/jdn005
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© 2008 London Mathematical Society

A Hurewicz theorem for the Assouad–Nagata dimension

N. Brodskiy and J. Dydak

University of Tennessee
Knoxville, TN 37996
USA
brodskiy@math.utk.edu

M. Levin

Departament of Mathematics
Ben-Gurion University of the Nagev
POB. 653
Beer-Sheba 84105
Israel
mlevine@math.bgu.ac.il

A. Mitra

University of Tennessee
Knoxville, TN 37996
USA
ajmitra@math.utk.edu

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.

The second and third authors were partially supported by Grant no. 2004047 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. The second author was partially supported by the Center for Advanced Studies in Mathematics at Ben Gurion University of the Negev (Beer-Sheva, Israel).

2000 Mathematics Subject Classification 54F45, 54C55 (primary), 54E35, 18B30, 54D35, 54D40, 20H15 (secondary).

Received May 29, 2006; revised April 29, 2007; published online March 14, 2008.


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