- #1
Avogadro Number
- 20
- 2
I am studying Choquet-Bruhat's Introduction to General Relativity, Black Holes and Cosmology, and I don't follow the hint in Exercise I.2.1:
Exercise I.2.1 Let U,V be open subsets of R^d. Prove that a C^1 diffeomorphism f:U-->V with f of class C^k is a C^k diffeomorphism.
Hint: ##\partial (f f^{-1})/ \partial x^i \equiv 0##.
Isn't f f^{-1} the identity map, and then how is the claimed partial identically zero? And how is this useful? Are we then meant to use the Chain Rule?
I would be grateful for any help! Thanks!
[Moderator's note: Moved from SR/GR.]
Exercise I.2.1 Let U,V be open subsets of R^d. Prove that a C^1 diffeomorphism f:U-->V with f of class C^k is a C^k diffeomorphism.
Hint: ##\partial (f f^{-1})/ \partial x^i \equiv 0##.
Isn't f f^{-1} the identity map, and then how is the claimed partial identically zero? And how is this useful? Are we then meant to use the Chain Rule?
I would be grateful for any help! Thanks!
[Moderator's note: Moved from SR/GR.]
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