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fiber bundle

In mathematics, and particularly topology, a fiber bundle (or, in Commonwealth English: fibre bundle) is a space that is locally a product space, but globally may have a different topological structure. Specifically, the similarity between a space E and a product space B × F is defined using a continuous surjective map, π : E → B , that in small regions of E behaves just like a projection from corresponding regions of B × F to B . The map π , called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space E is known as the total space of the fiber bundle, B as the base space, and F the fiber. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Fiber_bundle)

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