 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/f/f2/a/i/solution

C^{1}

R^{n}

f : U \to V

for which both

f

and

f^{- 1}

C^{k}

diffeomorphism requires that regularity for both maps; a smooth diffeomorphism has derivatives of every order. In the

C^{1}

setting used here,

f bijective, f, f^{- 1} \in C^{1} .

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