Locally trivial fibre bundle
A fibre bundle (cf. Fibre space) with fibre such that for any point of the base there is a neighbourhood and a homeomorphism such that , where , . The mapping is called a chart of the locally trivial bundle. The totality of charts associated with a covering of the base forms the atlas of the locally trivial bundle. For example, a principal fibre bundle with a locally compact space and a Lie group is a locally trivial fibre bundle, and any chart satisfies the relation
where acts on according to the formula . For any locally trivial fibre bundle and continuous mapping the induced fibre bundle is locally trivial.
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|||N.E. Steenrod, "The topology of fibre bundles" , Princeton Univ. Press (1951)|
|||S.-T. Hu, "Homotopy theory" , Acad. Press (1959)|
|||D. Husemoller, "Fibre bundles" , McGraw-Hill (1966)|
Locally trivial fibre bundle. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Locally_trivial_fibre_bundle&oldid=13769