2006/05/20 by Jerzy Dydak, J. Dydak, Dydak, J. +3
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #math.FA #math.MG
paper · pdf · doi:10.48550/arxiv.math/0605562
13 pages
arxiv created 2006/05/20 · openalex publication_date 2006/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
John Roe \citeRoe lectures introduced coarse structures for arbitrary sets X by considering subsets of X× X. That definition, while natural for analysts, is a bit more difficult to digest for topologists and geometers. In this paper we introduce large scale structures on X via the notion of uniformly bounded families and we show their equivalence to coarse structures on X. That way all basic concepts of large scale geometry (asymptotic dimension, slowly oscillating functions, Higson compactification) have natural definitions and basic results from metric geometry carry over to coarse geometry.