Asymptotic cones and Assouad-Nagata dimension

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dc.creatorDydak, J.
dc.creatorHiges, J.
dc.date2006-10-10
dc.date2006-10-20
dc.date.accessioned2026-07-07T12:12:32Z
dc.date.available2026-07-07T12:12:32Z
dc.descriptionWe prove the dimension of any asymptotic cone over a metric space X does not exceed the asymptotic Assouad-Nagata dimension of X. This improves a result of Dranishnikov and Smith who showed that dim(Y) does not exceed asymptotic Assouad-Nagata dimension of X for all separable subsets Y of special asymptotic cones of X over an exponential ultrafilter. We also show that Assouad-Nagata dimension of the discrete Heisenberg group equals its asymptotic dimension.
dc.description11 pages, comments from Behrstock, Brodskiy, Dranishnikov included
dc.identifierhttps://arxiv.org/abs/math/0610338
dc.identifierhttp://arxiv.org/abs/math/0610338
dc.identifierProceedings of the American Math.Soc. 136 (2008), 2225--2233
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210575
dc.subjectMetric Geometry
dc.subjectGeometric Topology
dc.titleAsymptotic cones and Assouad-Nagata dimension
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