Do diffeomorphisms have to be one-to-one functions?

[Antineutrino]

The definition of a diffeomorphism involves the differentiable inverse of a function, so must the original function be one-to-one to make its inverse a function, or can the inverse be a relation and not a function?

Sorry if it's a silly question, I am just a second semester calc student who looked at this for fun.

 

[PeroK]

The definition of a diffeomorphism involves the differentiable inverse of a function, so must the original function be one-to-one to make its inverse a function, or can the inverse be a relation and not a function?

Sorry if it's a silly question, I am just a second semester calc student who looked at this for fun.

If a function is not one-to-one, then it has no inverse.