2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70138We construct a infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie pseudogroup of infinite type is a regular infinite-dimensional Lie group, modelled on a locally convex strict inductive limit of Banach spaces. This is an infinite-dimensional generalization to the case of Lie pseudogroups of the classical second fundamental theorem of Lie.To appear in International Mathematics Research Notices, 17 pagesDifferential Geometry58H05; 58B25text