\begin{definition}[Definition:Diffeomorphism]
Let $n$ and $k$ be natural numbers.
Let $U,V\subset \R^n$ be open sets.
Let $f : U \to V$ be a mapping.
Then $f$ is a '''$C^k$-diffeomorphism''' {{iff}} $f$ is a bijection of class $C^k$ with an inverse of class $C^k$.
\end{definition}