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vector bundle

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

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