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A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.

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Local diffeomorphism on a neighborhood of an embedding

Lemma 1: Let $N\subset F$ be a compact embedded submanifold of a smooth manifold $F$, and let $\nu: F \rightarrow E$ be a smooth map which is injective on $N$ and a local diffeomorphism at every $n\in …
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