fiber bundle
التعريفات والمعاني
== English ==
=== Alternative forms ===
fibre bundle (British)
=== 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.
=== Noun ===
fiber bundle (plural fiber bundles)
(botany) Synonym of vascular bundle.
(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
π
{\displaystyle \pi }
from E to B (called the projection or submersion), such that every point of B has a neighborhood U with
π
−
1
(
U
)
{\displaystyle \pi ^{-1}(U)}
homeomorphic to the product space U
×
{\displaystyle \times }
F (that is, E looks locally the same as the product space B
×
{\displaystyle \times }
F, although its global structure may be quite different).
==== Usage notes ====
Properly, a fiber bundle is either the tuple (E,
π
{\displaystyle \pi }
,B), the tuple (E,
π
{\displaystyle \pi }
,B,F), or the map
π
{\displaystyle \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 ====
(topological space): bundle
==== Hyponyms ====
(topological space): vector bundle
==== Meronyms ====
(topological space): base space, fiber, cross section
==== Translations ====
=== See also ===
associated bundle
base space
fiber space
fibration
principal bundle
structure group
total space
trivial bundle
=== References ===
=== Further reading ===
Bundle (mathematics) on Wikipedia.Wikipedia
fiber bundle on nLab
Fiber Bundle on Wolfram MathWorld
Fibre space on Encyclopedia of Mathematics
Bundle on Encyclopedia of Mathematics
1951, Norman Steenrod, The Topology of Fibre Bundles, Princeton University Press (standard reference)
=== Anagrams ===
fibre bundle, lubber fiend