Fiber bundle construction theorem

The fiber bundle construction theorem is a fundamental result in differential geometry and algebraic topology that provides a way to construct fiber bundles from certain types of spaces. A fiber bundle is a structure that consists of a total space, a base space, a projection map, and a typical fiber that is consistent across the base space. While the theorem itself can be stated in several ways depending on context, it generally concerns the relationship between certain types of spaces and their ability to form fiber bundles under specific conditions.