Thread: diffeomorphism

Looking for help with a textbook problem.

Give an example to demonstrate that a one-to-one and onto mapping need not be a diffeomorphism. (Hint: Take )

I'm assuming that the hint means let

I'm very stuck, however and having trouble thinking this through. Help and/or a couple of examples would be greatly appreciated.

Take F(x)= x/(x+1) for x in [0,1] and F(x)=x for x>1.
(reflect this to the negative side).
I believe it's injective and onto, but F its derivative at x=1 isn't defined.
( and ).

Originally Posted by Zennie

Give an example to demonstrate that a one-to-one and onto mapping need not be a diffeomorphism. (Hint: Take )

For example,


Fernando Revilla