Orbits of Lie Group Actions are Weakly Embedded
  In this note we prove that whenever a Lie group $G$ acts on a manifold $X$, then the orbit $Gx$ through any point $x$ of $X$ is a weakly embedded submanifold of $X$. The investigation of this problem was inspired by an application to Cat astrophe Theory. 
Domenico P.L. Castrigiano, Sandra A. Hayes