2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68920For a finite dimensional Lie algebra $\g$ of vector fields on a manifold $M$ we show that $M$ can be completed to a $G$-space in a unversal way, which however is neither Hausdorff nor $T_1$ in general. Here $G$ is a connected Lie group with Lie-algebra $\g$. For a transitive $\g$-action the completion is of the form $G/H$ for a Lie subgroup $H$ which need not be closed. In general the completion can be constructed by completing each $\g$-orbit.10 pages, LatexDifferential Geometry22F05, 37C10, 54H15, 57R30, 57S05, 58A40text