Pullback bundle

In mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle $π : E \to B$ and a continuous map $f : B' \to B$ one can define a "pullback" of $E$ by $f$ as a bundle $f * E$ over $B'$ . The fiber of $f * E$ over a point $b'$ in $B'$ is just the fiber of $E$ over $f (b')$ . Thus $f * E$ is the disjoint union of all these fibers equipped with a suitable topology.

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