For questions about fiber bundle, which is a space that is locally a product space, but globally may have a different topological structure.
In mathematics, a fiber bundle (or, in British 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: $\pi \colon E \to B$ 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.
