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...
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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