Fiber bundle

English

Alternative forms

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Etymology

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

Noun

1. Template:Lb 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).

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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.

Hypernyms

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Hyponyms

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Meronyms

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Translations

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See also

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Further reading

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• fiber bundle on Template:W
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• Fibre space on Template:W
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• 1951, Template:W, The Topology of Fibre Bundles, Template:W Template:Qualifier

Anagrams

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