2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158027We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced function between the nonstandard hulls is smooth. We also discuss some conditions on a function between locally convex spaces which guarantee that its nonstandard extension maps finite points to finite points.Differential GeometryLogic22E65; 26E35text