In mathematics, a pullback bundle or induced bundle is a useful construction in the theory of fiber bundles. Given a fiber bundle π : E → B and a continuous map f : B′ → 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 x in B′ is just the fiber of E over f(x). Thus f *E is the disjoint union of all these fibers equipped with a suitable topology.
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