This question from a previous paper of an exam I am studying for.
Let $G$ be a lie group. Let $\pi$ be a continuous representation of $G$ in $V$ a finite dimensional complex linear space. Let $W$ be a linear subpsace of $V$. Show that $H:=\{x\in G: \pi(x)W \subset W\}$ is closed in $G$.
I'm very stuck trying to tackle this question. If we restrict $\pi$ to $H$ then it gives that $W$ is invariant, but I cannot see how this helps.