Let $X$ be a compact, path-connected subset of $\mathbb{R}^n$. I need a reference for the fact that the $n$-th homotopy group $\pi_n(X)$ is trivial.
EDIT: Quite embarrassing. Indeed this is false, as the comment below indicates ($\pi_3(S^2)=\mathbb{Z}$). Should have thought more before posting the question.