"Calculus on Manifolds", Proof of Change of Variables theorem.
I don't understand how letting $U=k^{-1}(V)$ leads to $h(U)\subset V$. It would most definitely make sense if we let $U=h^{-1}(V)$
2026-03-31 04:17:21.1774930641
Error in Spivak's "Calculus on Manifolds". Construction of function composition for proof of change of variables
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You are right, it is a typo. $k$ is defined on $h(U')$ and we have $h(a) \in V \subset h(U')$, thus we must of course take $U =h^{-1}(V) \subset U'$ in order to get $h(U) \subset V$.