2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228073We determine the set of Busemann points of an arbitrary finite-dimensional normed space. These are the points of the horofunction boundary that are the limits of "almost-geodesics". We prove that all points in the horofunction boundary are Busemann points if and only if the set of extreme sets of the dual unit ball is closed in the Painleve-Kuratowski topology.11 pages v2. Some proofs streamlined and another example addedGeometric TopologyMetric Geometry53C23 (Primary) 51B20, 20F65 (Secondary)text