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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.
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oh now i see. compactness of source space implies surjectivity (replied to myself here in case anybody had the same doubt).
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Thus, in general, I am not sure how a local diffeomorphism (that is not a diffeomorphism) might arise from a flow.
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