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 X {\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} .