fiber bundle in German

(American spelling, topology, category theory) An abstract object in topology where copies of one object are "attached" to every point of another, as hairs or fibers are attached to a hairbrush. Formally, a topological space E (called the total space), together with a topological space B (called the base space), a topological space F (called the fiber), and surjective map \pi from E to B (called the projection or submersion), such that every point of B has a neighborhood U with \pi^{-1}(U) homeomorphic to the product space U \times F (that is, E looks locally the same as the product space B \times F, although its global structure may be quite different).