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. |
Classroom Articles on Topology (Up to Graduate Level)
