# Vector Bundle

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.

Vector bundle is a graduate-level concept that would be first encountered in a topology course.

### Examples

Tangent Bundle: | In topology, a tangent bundle of a given manifold is a new manifold that consists of the tangent spaces for each point pasted together in a continuous fashion. |

### Prerequisites

Manifold: | A manifold is a topological space that is locally Euclidean, i.e., around every point, there is a neighborhood that is topologically the same as an open unit ball in some dimension. |

Topological Space: | A topological space is a set with a collection of subsets T that together satisfy a certain set of axioms defining the topology of that set. |

Vector Space: | A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |