2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63601We give a characterization of extremal sets in Hilbert spaces that generalizes a classical theorem of H. W. E. Jung. We investigate also the behaviour of points near to the circumsphere of such a set with respect to the Kuratowski and Hausdorff measures of non-compactness.10 pages, corrected some misprintsMetric GeometryFunctional Analysis46B20, 46E30text