Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a pullback bundle or induced bundle is a useful construction in the theory of fiber bundles. Given a fiber bundle : 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. In mathematics, and particularly topology, a fiber bundle (or, in BrE, fibre bundle) is intuitively a space E which locally "looks" like a product space B x F, but globally may have a different topological structure. Specifically, the similarity between the fiber bundle E and a product space B x F is defined using a continuous surjective map picolon E to B that in small regions of E behaves just like a projection from corresponding regions of B x F to B.

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