Exercise · ZW-SMOOTH-DIFFEOMORPHIC-DEFORMATION-001 · ★★☆ Intermediate

A map \(\varphi:M\to N\) is a candidate to be a diffeomorphism, but its inverse turns out to be only continuous and not smooth. Which conclusion is correct?

Choose one option.

1. AIt is not a diffeomorphism, because smoothness of \(\varphi^{-1}\) is also required
2. BIt is a diffeomorphism, because it is enough for \(\varphi\) to be bijective
3. CIt is automatically an isometry
4. DIt cannot be a function

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