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Revista Matemática Complutense

, Volume 29, Issue 1, pp 191–206 | Cite as

Preserving coarse properties

  • J. Dydak
  • Ž. Virk
Article

Abstract

The aim of this paper is to investigate properties preserved and co-preserved by coarsely n-to-1 functions, in particular by the quotient maps \(X\rightarrow X/\sim \) induced by a finite group G acting by isometries on a metric space X. The coarse properties we are mainly interested in are related to asymptotic dimension and its generalizations: having finite asymptotic dimension, asymptotic Property C (as defined by Dranishnikov in Rus. Math. Surv. 55(6):1085–1129, 2000), straight finite decomposition complexity, countable asymptotic dimension, and metric sparsification property. We provide an alternative description of asymptotic Property C and we prove that the class of spaces with straight finite decomposition complexity coincides with the class of spaces of countable asymptotic dimension.

Keywords

Asymptotic dimension Asymptotic Property C Coarse geometry Coarsely n-to-1 functions Lipschitz maps  Metric sparsification property Straight finite decomposition complexity 

Mathematics Subject Classification

Primary 54F45 Secondary 55M10 

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Copyright information

© Universidad Complutense de Madrid 2015

Authors and Affiliations

  1. 1.University of TennesseeKnoxvilleUSA
  2. 2.Univerza v LjubljaniLjubljanaSlovenia

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