2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135802A systematic review of the various topologies that can be defined on the projective Hilbert space P(H), i.e., on the set of the pure quantum states, is presented. It is shown that P(H) carries a natural topology as well as a natural measurable structure.11 pagesMathematical Physics46N50, 81Q99, 54H99, 28C15Topologies and Measurable Structures on the Projective Hilbert Spacetext