Bundle Maps Over A Common Base
Let πE:E→ M and πF:F→ M be fiber bundles over a space M. Then a bundle map from E to F over M is a continuous map φ:E→ F 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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