What is a Diffeomorphism in Match?

What is a diffeomorphism and how I can write this in one equation?

I know what is a homomorphism and I write it as fallow:

∀x,y∈Xf(x+y)=f(x)+f(y)\forall_{x,y\in X} f(x+y)=f(x)+f(y).

Could somebody help me?

=================

A diffeomorphism is a little more complicated: en.wikipedia.org/wiki/Diffeomorphism
– Joe Johnson 126
Oct 20 at 19:36

=================

=================