# Diffeomorphism

From Maths

## Definition

A *diffeomorphism*^{[1]} is a special kind of homeomorphism, a function [ilmath]f[/ilmath] is said to be a diffeomorphism if:

- [ilmath]f[/ilmath] is bijective
- [ilmath]f[/ilmath] is smooth (all partial derivatives of all orders are continuous)
- [ilmath]f^{-1} [/ilmath] is also smooth

## References

- ↑ Introduction to smooth manifolds - John M Lee - Second Edition