2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119163We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study classical invariants of general topological spaces.13 pagesAlgebraic Topology55P10, 55P15, 18B35, 18G30text