Let Let $E \rightarrow X$ be a vector bundle on a manifold $X$. Let $\cal E$ be the sheaf of sections of $E$. Let $\cal F$ be a subsheaf of $\cal E$, and let $F$ be the etale space of $\cal F$. What is an example that the map $F \rightarrow E$ might not be an injection on all fibers?
Subbundles and subsheaves
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differential-topology
sheaf-theory