General Morphisms of Fiber Bundles
Let πE:E→ M and πF:F→ N be fiber bundles over spaces M and N respectively. Then a continuous map φ:E→ F is called a bundle map from E to F if there is a continuous map f:M→ N such that the diagram
commutes, that is, . In other words, φ is fiber-preserving, and f is the induced map on the space of fibers of E: since πE is surjective, f is uniquely determined by φ. For a given f, such a bundle map φ is said to be a bundle map covering f.
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