Fiber bundles

A fiber bundle is a mathematical structure where, around each point of a space (called the base), there's a related space called a fiber that varies smoothly from point to point. Imagine a surface like a sphere, and at each point, attach a small object (the fiber) such as a circle or a line. This setup helps describe complex shapes and fields, especially in physics and geometry, by combining local data (fibers) into a global structure that reflects how the fibers are arranged across the entire base space.