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Definition/Summary
Intuitively speaking, a fibre bundle is space E which ‘locally looks like’ a product space B×F, but globally may have a different topological structure.
Extended explanation
Definition:
A fibre bundle is the data group (E, B,\pi, F), where E, B, and F are topological spaces called the total space, the base space, and the fibre space, respectively and \pi : E \rightarrow B is a continuous surjection, called the projection, or submersion of the bundle, satisfying the local triviality condition.
(We assume the base space B to be connected.)
The local triviality condition states the following:
we require that for any x \in E that there exist an open neighborhood, U of \pi (x) such that \pi^-1(x) is homeomorphic to the product space U×F in such a manner as to...
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