Solution
= Solution
A <submersion> from a nonempty compact manifold to $\mathbb R^\ell$, $\ell\ge1$, would be surjective by the preceding result, since the target is connected. Its image would also be compact, contradicting noncompactness of $\mathbb R^\ell$. Thus \b[no such submersion exists]. The nonempty-domain qualification excludes the vacuous empty-manifold case.