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Wiktionary英語版での「fiber bundle」の意味 |
fiber bundle
別の表記
語源
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 かつ gefaserter Räume) from 1933, Herbert Seifert, “Topologie dreidimensionaler gefaserter Räume,” Acta Mathematica, 60, (1933), 147-238.[1][2]
名詞
fiber bundle (複数形 fiber bundles)
- (米国用法 spelling, topology, category theory) A topological space E with a base space B and a fiber space F such that any point x ∈ B has a neighborhood N that is homeomorphic to the product space B × F (that is, the space is locally the product space B × F, although its global structure can be quite different).
- 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 (a Möbius strip かつ a cylinder have isomorphic base spaces). A Klein bottle is a fiber bundle which looks locally like the corresponding part of a torus (again they could be thought of as sharing the same base space ; cutting out even a single point of that base space makes the cut Klein bottle isomorphic to the cut torus).
- 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.
- 1995, Sunny Y. Auyang, How is Quantum Field Theory Possible?, Oxford University Press, page 214,
- In the 1960s, some physicists including E. Lubkin and A. Trautman recognized that interaction potentials can be represented by connections on principal fiber bundles. In 1975, T. T. Wu and C. N. Yang used the fiber bundle method to solve a problem on magnetic monopoles.
- 2001, John M. May, Parallel I/O for High Performance Computing, Morgan Kaufmann Publishers, page 236,
- One proposed general model for high-level scientific data uses fiber bundles, which Butler and Pendley [22] proposed in 1989. […] A fiber bundle is the Cartesian product of the fibers and the base space; in other words, it is the collection of valid data ranges for the base space.
- 2013, Patrick Iglesias-Zemmour, Diffeology, American Mathematical Society, page 229,
- Finding the right notion of fiber bundle for diffeology [Igl85] has been a question raised by the study of the irrational torus [Dolg85].
使用する際の注意点
May be defined formally as the tuple (or sometimes ), where , and are topological spaces respectively called the total space, base space and fiber space, and is a continuous surjective map called the projection or submersion of the fiber bundle or fiber space. The fiber bundle is sometimes formally identified as the map , with and being assumed from its definition.
上位語
- (topological space): bundle
下位語
Meronyms
参考
参照
Further reading
- Bundle (mathematics) on 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)
アナグラム
「fiber bundle」の部分一致の例文検索結果
該当件数 : 1805件
CARBON FIBER BUNDLE FOR WOVEN FABRIC例文帳に追加
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