Bundle Map - Bundle Maps Over A Common Base

Bundle Maps Over A Common Base

Let πE:EM and πF:FM be fiber bundles over a space M. Then a bundle map from E to F over M is a continuous map φ:EF such that . That is, the diagram

should commute. Equivalently, for any point x in M, φ maps the fiber Ex = πE−1({x}) of E over x to the fiber Fx = πF−1({x}) of F over x.

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