Diffeomorphism

Statements

Definition. Let $r\in {\mathbb{N}}_{>0}$, $U$ and $V$ be open sets of ${\mathbb{R}}^n$. A vector-valued function $F:U\to V$ is said to be a ${\mathcal{C}}^r-$diffeomorphism if

1. $F$ is a homeomorphism.
2. $F$ and $F^{-1}$ are of class ${\mathcal{C}}^r(U,V)$.

References

• @GodNat14 pp. 12
• @Boo75 Sectin 2.6