2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210575We 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.11 pages, comments from Behrstock, Brodskiy, Dranishnikov includedMetric GeometryGeometric Topologytext