I am a beginner in manifold. I am reading Push forward map ( or differential map at a point). I came across the following question:
Give smooth maps $F: M \to \mathbb{R^3}$ and $G: N \to \mathbb{R^3}$ where Manifolds $M$ and $N$ are not open subset of $\mathbb{R^3}$ such that the push forward maps induced a point $p$, that is $F_{*},p : T_{p}M \to T_{p} \mathbb{R^3}$ and $G_{*},p : T_{p}N \to T_{p} \mathbb{R^3}$ are not constant maps.
My attempt:
My idea is to take $M=S^3$( which is not open in $\mathbb{R^3})$ now I tried to define a smooth map $F: M \to \mathbb{R^3}$ but I got stuck.
Thanks for any insight!!