# Locally trivial fibre bundle

From Encyclopedia of Mathematics

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.

#### References

[1] | E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) |

[2] | N.E. Steenrod, "The topology of fibre bundles" , Princeton Univ. Press (1951) |

[3] | S.-T. Hu, "Homotopy theory" , Acad. Press (1959) |

[4] | D. Husemoller, "Fibre bundles" , McGraw-Hill (1966) |

**How to Cite This Entry:**

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

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098