Bundle map

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This article defines a property of continuous maps between topological spaces

Definition

A surjective continuous map p:E \to B is termed a bundle map or fiber bundle with fiber F (where F is an abstract topological space) if the following is true:

  • The fiber at any point is homeomorphic to F
  • Every point in B has an open neighbourhood U such that the map p^{-1}(U) \to U looks like the projection U \times F \to U (this is called a local triviality condition)

If there is a homeomorphism from E to B \times F under which p gets sent to the projection map, then we say that the bundle map is trivial.

Relation with other properties

Stronger properties

Weaker properties

Incomparable properties