# Fiber Bundle

In mathematics, and particularly topology, a fiber bundle (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 {\displaystyle E} and a product space B × F {\displaystyle B\times F} is defined using a continuous surjective map, π : E → B , {\displaystyle \pi :E\to B,} that in small regions of E {\displaystyle E} behaves just like a projection from corresponding regions of B × F {\displaystyle B\times F} to B . {\displaystyle B.} The map π , {\displaystyle \pi ,} called the projection or submersion of the bundle, is regarded as part of the structure of the bundle.