# Diffeomorphism

Jump to: navigation, search

## 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

1. Introduction to smooth manifolds - John M Lee - Second Edition