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 (for example
X could be a
topological space, a
manifold, or an
algebraic variety): to every point
x of the space
X we associate (or "attach") a vector space
V(
x) in such a way that these vector spaces fit together to form another space of the same kind as
X (e.g. a topological space, manifold, or algebraic variety), which is then called a
vector bundle over X.