fiber bundle

A fiber bundle is a mathematical concept that describes a space made up of a "base" space (like a surface or shape) and, attached to each point of this base, a smaller "fiber" space (such as a line or a circle). Imagine attaching a small fiber (like a tiny thread or circle) at every point of a surface, where these fibers vary continuously across the surface. Fiber bundles are useful for understanding complex structures in geometry, physics, and engineering, providing a framework to study how local parts (fibers) are organized over a whole space (base).