2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170173The sets of closed and closed-normal subgroups of a profinite group carry a natural profinite topology. Through a combination of algebraic and topological methods the size of these subgroup spaces is calculated, and the spaces partially classified up to homeomorphism.Group TheoryGeneral Topology54H05, 03E15, 28A05text