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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. — 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)