True or false? Let $f:M \longrightarrow N $ map $C^{\infty}$ bijective, where $M$ and $N$ are manifolds de class $C^{\infty}$, then $f$ is a diffeomorphism.
Comments:
I am thinking of making a restriction on the function $\pi: S^n \longrightarrow \mathbb{R}P^n$, but I do not know if this works because it diffeomorphism local.