2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114173For a large class of metric space X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdim X of X coincides with the covering dimension $\dim(ν_L X)$ of the Higson corona of X with respect to the sublinear coarse structure on X. Then we apply this fact to prove the equality AN-asdim(X x R) = AN-asdim X + 1. We note that the similar equality for Gromov's asymptotic dimension asdim generally fails to hold [Dr3]. Additionally we construct an injective map from the asymptotic cone without the basepoint to the sublinear Higson Corona.28 pages, 0 figuresMetric GeometryGeometric Topology51F99; 54F45text