2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129950A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two properties. This answers a question of Sela.39 pages, 4 figures, added a double-coset-separability result, to appear in GAFAGroup TheoryGeometric Topology20F65 (20E26, 20E05)text