Prove that $\mathbb{S}^n \times \mathbb{S}^k$ is diffeomorphic to a submanifold of $\mathbb{R}^{n+k+1}$.
$\mathbb{S}^n \times \mathbb{S}^k \subset \mathbb{R}^{n+1} \times \mathbb{R}^{k+1}=\mathbb{R}^{n+k+2}$. It's known that $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{R}^{n+1} \setminus \{0\}$ are diffeomorphic.
but I don't know how to use these facts to solve the exercise, any help please