Fiber bundle

Summary

A fiber bundle is a space that looks locally like a product of a base space and a fixed fiber, but may be twisted globally. It comes with a projection to the base whose preimages, the fibers, are all copies of the same space. Vector bundles, covering spaces, principal bundles and the Hopf fibration are all fiber bundles. They describe families of spaces parametrized by a base, and they are central in topology, geometry and physics.