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I thank the kind person who induced me to put this question to rest by a downvote. ;) I admit the question was caused by an extremely silly oversight owing to severe sleep deprivation, but surely we are all allowed at least once in our lives to make fools of ourselves on the internet for posterity to laugh at. As @Hurkyl has pointed out in comments, the ...


Let $p : E \to B$ be a (real for example) vector bundle. It's locally trivial, meaning that if you take a small open set $U \subset B$, then you can find an isomorphism $\varphi : p^{-1}(U) \cong U \times \mathbb{R}^n$, compatible with $p$ (meaning that $\varphi(\xi) = (p(\xi), \text{something})$). Now a section $s : B \to E$ of $p$ is a map such that $p ...

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