Given a topological space X, a vector bundle is a way of associating a vector space to each point of X in a consistent way.

U×R^n, are fiber-for-fiber vector space isomorphisms. A vector bundle is a total space E along with a surjective map π:E->B to a base manifold B. Any fiber π^(-1)(b) is a vector space isomorphic to V. The simplest nontrivial vector bundle is a line bundle on the circle, and is analogous to the Möbius strip." style="margin-top: 7px;" />

bundle rank | fiber | fiber bundle | Hermitian metric | K-theory | Lie algebroid | linear algebra | principal bundle | Riemannian metric | stable equivalence | tangent bundle | tangent map | trivial bundle | vector bundle connection | vector space | Whitney sum

graduate school level