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my little problem is :

Let E be a vector bundle over a manifold M, and (s_ {1}, ......, s_ {n}) a family of sections of E. This family is generating bundle E, that is for every point x in M, (s_ {1} (x), ......, s_ {n} (x)) is generator of the vector space E_{x} ? is that we have only (s_ {1} (x1), ......, s_ {n} (x1)) is a generator of E_ {x1} and (s_ {1} (x 2), .. ...., s_ {n} (x2)) is not generating E_ {x2}??

Thank you for making me understand this confusion on sections of a vector bundle generator ...

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# Sections of the vector bundle

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