Talk:Local diffeomorphism

i don't get the example of the 2-sphere and euclidean plane in the discussion section: a local diffeomorphism is not required to be onto, so i see no contradiction in the fact that the image of the 2-sphere under the local diffeo is compact. please can someone explain? thanks. — Preceding unsigned comment added by 147.122.45.24 (talk) 19:51, 5 July 2011 (UTC)

oh now i see. compactness of source space implies surjectivity (replied to myself here in case anybody had the same doubt).147.122.45.24 (talk) 20:00, 5 July 2011 (UTC)

on the empty section "Local flow diffeomorphisms"
Given a vector field on a manifold $$X$$, we have its time-$$t$$ local flow $$\Phi^t$$. This will be a "locally-defined" diffeomorphism, namely a diffeomorphism between open subsets of $$X$$. If $$\Phi^t$$ is defined on all of $$X$$, the it is a diffeomorphism.

Thus, in general, I am not sure how a local diffeomorphism (that is not a diffeomorphism) might arise from a flow. SkiingArcher (talk) 23:58, 11 June 2024 (UTC)