Let *π* : *E* → *B* be a fiber bundle with abstract fiber *F* and let *f* : *B*′ → *B* be a continuous map. Define the **pullback bundle** by

and equip it with the subspace topology and the projection map *π*′ : *f*^{*}*E* → *B*′ given by the projection onto the first factor, i.e.,

The projection onto the second factor gives a map

such that the following diagram commutes:

If (*U*, φ) is a local trivialization of *E* then (*f*^{−1}*U*, ψ) is a local trivialization of *f*^{*}*E* where

This page was last edited on 21 May 2018, at 00:53 (UTC).

Reference: https://en.wikipedia.org/wiki/Pullback_bundle under CC BY-SA license.

Reference: https://en.wikipedia.org/wiki/Pullback_bundle under CC BY-SA license.

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