2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223073We show that if the Banach-Mazur distance between an n-dimensional normed space X and ell infinity is at most 3/2, then there exist n+1 equidistant points in X. By a well-known result of Alon and Milman, this implies that an arbitrary n-dimensional normed space admits at least e^{c sqrt(log n)} equidistant points, where c>0 is an absolute constant. We also show that there exist n equidistant points in spaces sufficiently close to n-dimensional ell p (1 < p < infinity).5 pagesMetric GeometryFunctional Analysis46B04 (Primary); 46B20, 52A21, 52C17 (Secondary)text