👉 In mathematics, a fiber bundle is an algebraic structure that allows for the construction of parallel bundles. These bundles are useful in various areas such as physics, engineering and computer science. A fiber bundle consists of two spaces X and Y, where each space X can be thought of as a topological space, while Y is a smooth manifold (or more generally a manifold with boundary). The fibers of the bundle are smooth manifolds that are homeomorphic to X. The main properties of fiber