fiber bundle

Etymology
Coined as by American mathematician  in 1951, The Topology of Fibre Bundles. The related usages and  probably derive (as calques respectively of German  and ) from 1933,, “Topologie dreidimensionaler gefaserter Räume,” Acta Mathematica, 60, (1933), 147-238.

Noun

 * 1)  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).

Usage notes
Properly, a fiber bundle is either the tuple (E,$$\pi$$,B), the tuple (E,$$\pi$$,B,F), or the map $$\pi$$ alone (which formally contains E and B in its definition). Sometimes, by ˞˞˞˞abuse of notation, E maybe referred to as a fiber bundle.

Translations

 * Catalan: fibrat
 * Finnish: kuitukimppu
 * German: Faserbündel
 * Korean: 올다발
 * Portuguese: fibrado