Let $\Omega \subset \mathbb{R}^n$ be a bounded (not necessarily connected) set with $C^2$-boundary $\partial \Omega$. Then $\Omega$ can only have finitely many connected components.
↧
Let $\Omega \subset \mathbb{R}^n$ be a bounded (not necessarily connected) set with $C^2$-boundary $\partial \Omega$. Then $\Omega$ can only have finitely many connected components.