fiber bundle
nounEtymology
(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.
- derived from Faser and gefaserter Räume) from 1933
Definitions
Synonym of vascular bundle.
An abstract object in topology where copies of one object are "attached" to every point…
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).
- In general, a fiber bundle consists of a set of mutually disjoint fibers “over” a base space, which indexes the fibers; there is a copy of some fiber on top of, or projecting (“canonically”) onto each point of the base space.
The neighborhood
- neighborassociated bundle
- neighborbase space
- neighborfiber space
- neighborfibration
- neighborprincipal bundle
- neighborstructure group
- neighbortotal space
- neighbortrivial bundle
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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA