A $C^1$ <diffeomorphism> $F:U\to V$ is a <bijection> for which both $F$ and $F^{-1}$ are continuously differentiable. If a higher regularity class is specified, both maps must belong to that class. In particular, a <diffeomorphism> is a <homeomorphism>, and the <chain rule> gives $D(F^{-1})(F(x))=(DF(x))^{-1}$.

Solution

Past exam of the options I for mathematics and philosophy course of the University of Oxford / 2013 / F / 1 / c / i / Solution

 Solution (source code)