This may be a stupid question, but I have not seen anywhere that it is said that a diffeomorphism must be an immersion and a submersion. Therefore I am asking the following two questions:
(I) Is a diffeomorphism between smooth manifolds necessarily a submersion?
(II) Is a diffeomorphism between smooth manifolds necessarily an immersion?
(III) If either (I) or (II) aren't true, can someone help by giving a counter example?
Thanks in advance.