Completing Lie algebra actions to Lie group actions

For a finite dimensional Lie algebra $\text{g}$ 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 $\text{g}$. For a transitive $\text{g}$-action the completion is of the form $G\mathrm{/}H$ for a Lie subgroup $H$ which need not be closed. In general the completion can be constructed by completing each $\text{g}$-orbit.