An alternative definition of coarse structures

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dc.creatorDydak, J.
dc.creatorHoffland, C. S.
dc.date2006-05-20
dc.date.accessioned2026-07-07T07:14:25Z
dc.date.available2026-07-07T07:14:25Z
dc.descriptionJohn Roe \cite{Roe lectures} introduced coarse structures for arbitrary sets $X$ by considering subsets of $X\times X$. 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.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0605562
dc.identifierhttp://arxiv.org/abs/math/0605562
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112870
dc.subjectMetric Geometry
dc.subjectFunctional Analysis
dc.titleAn alternative definition of coarse structures
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