2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221915We show that the unit ball of a Hilbert space in its weak topology is a continuous image of the countable power of the Alexandroff compactification of a discrete set, and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when the space is nonseparable.General TopologyFunctional Analysis46B50, 46B26, 46C05, 54B30, 54D15.text