2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60458In 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.5 pagesDifferential Geometrytransformation groups, manifoldstext