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Fiber bundle
Definitions
- 1 Synonym of vascular bundle.
- 2 a bundle of fibers (especially nerve fibers) wordnet
- 3 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 π from E to B (called the projection or submersion), such that every point of B has a neighborhood U with π⁻¹(U) homeomorphic to the product space U × F (that is, E looks locally the same as the product space B × F, although its global structure may be quite different). US
"A Möbius strip is a fiber bundle which looks locally (i.e., over a connected proper subset of its base space) like the corresponding part of a cylinder S¹#92;times#91;0,1#93; (a Möbius strip and a cylinder have isomorphic base spaces). A Klein bottle is a fiber bundle which looks locally like the corresponding part of a torus S¹#92;timesS¹ (again they could be thought of as sharing the same base space S¹; cutting out even a single point of that base space makes the cut Klein bottle isomorphic to the cut torus)."
Etymology
(mathematics): Coined as fibre bundle by American mathematician Norman Steenrod in 1951, The Topology of Fibre Bundles. The related usages fiber and fiber space probably derive (as calques respectively of German Faser and gefaserter Räume) from 1933, Herbert Seifert, “Topologie dreidimensionaler gefaserter Räume,” Acta Mathematica, 60, (1933), 147-238.
See also for "fiber bundle"
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