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Let π:E→B be a smooth vector bundle. Prove π is a submersion.

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    Also, as user7887 noted below, local triviality of vector bundles implies $\pi$ is locally expressible as a canonical submersion, which means $\pi$ is a submersion. But usually these types of "definition-pushing" homework questions (assuming it is so) like this is tailored to the way various concepts are precisely defined in your class. So you should at least state in your question how you've seen submersion and vector bundle defined.2011-03-12

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We need to show locally $U$ of $E$ submerged to $V$ of $B$. But note $U\cong V\times F$, this should be automatic.

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    No, I don't. I'm a little confused on the definition because I haven't done it before. I get user7887's point on showing the isomorphism2011-03-13