  For 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.
