大学学部レベル質問スレ 24単位目

あ、今、『Caluculus on Manifolds』を見ていたら、


Problem 2-36
Let A ⊂ R^n be an open set and f : A → R^n a continuously differentiable 1-1 function such that det f'(x) ≠ 0 for all x.
Show that f(A) is an open set and f^{-1} : f(A) → A is differentiable.
Show also that f(B) is open for any open set B ⊂ A.

という問題がありました。