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Let $M,N$ be compact connected manifolds, $f:M \to N$ a smooth map with $\operatorname{rank}{(df)}=\dim{N}$. Then for all points $p,q \in N$ ; $f^{-1}p$ is diffeomorphic to $f^{-1}q$.

Please help me solve this question, I've no idea.

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    Surely you have some thoughts. For example what does the condition 'rank(df)=dim N' imply?2011-06-24
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    @wild: Good remark of yours. Unfortunately I am not sure one can *have some thoughts* and at the same time post **five** questions in a time span of one hour or so.2011-06-24
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    please make the body of your questions self-contained. It is customary here to state the question in the main body and not only in the title. Also, most of your questions seem to be relating more to differential geometry or differential topology than algebraic topology. Moreover, what kind of *homework* is this? It would be much easier for us to answer your questions if you provided a little bit of your own background and thoughts.2011-06-24
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    [Moved](http://meta.math.stackexchange.com/questions/2417/re-henrys-questions) to meta (and let's remove meta-comments from here, please)2011-06-24
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    In particular, please consult our [homework FAQ](http://meta.math.stackexchange.com/questions/1803/how-to-ask-a-homework-question) too see what other information you should include in a question like this to make it easier for other users to help you.2011-06-24

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