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Vector bundles

In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another spaceX{\displaystyle X} (for example X{\displaystyle X} could be a topological space, a manifold, or an algebraic variety): to every point x{\displaystyle x} of the space X{\displaystyle X} we associate (or "attach") a vector space V(x){\displaystyle V(x)} in such a way that these vector spaces fit together to form another space of the same kind as X{\displaystyle X} (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X{\displaystyle X}.

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