In mathematics, a pullback bundle or induced bundle[1][2][3] is the fiber bundle that is induced by a map of its base-space. 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 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.