Vector Bundle

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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.


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.


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)

  • Closed Set
  • Möbius Strip
  • Differential Topology
  • Neighborhood
  • Dimension
  • Open Set
  • Homeomorphism
  • Point-Set Topology
  • Homology
  • Projective Plane
  • Homotopy
  • Projective Space
  • Knot
  • Subspace
  • Link
  • Tangent Space
  • Metric
  • Topology
  • Metric Space
  • Torus