Solution
= Solution
A $C^1$ <diffeomorphism> between <open subsets> of $\mathbb R^n$ is a <bijection> $f:U\to V$ for which both $f$ and $f^{-1}$ are <continuously differentiable>. More generally, a $C^k$ <diffeomorphism> requires that regularity for both maps; a <smooth> <diffeomorphism> has <derivatives> of every order. In the $C^1$ setting used here,
$$
\boxed{f\text{ bijective},\qquad f,f^{-1}\in C^1.}
$$