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In mathematics, a pullback bundle or induced bundle〔 〕 is a useful construction in the theory of fiber bundles. Given a fiber bundle and a continuous map one can define a "pullback" of by as a bundle over . The fiber of over a point in is just the fiber of over . Thus is the disjoint union of all these fibers equipped with a suitable topology. ==Formal definition== Let be a fiber bundle with abstract fiber and let be a continuous map. Define the pullback bundle by : and equip it with the subspace topology and the projection map given by the projection onto the first factor, i.e., : The projection onto the second factor gives a map : such that the following diagram commutes: : If is a local trivialization of then is a local trivialization of where : It then follows that is a fiber bundle over with fiber . The bundle is called the pullback of ''E'' by or the bundle induced by . The map is then a bundle morphism covering . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「pullback bundle」の詳細全文を読む スポンサード リンク
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