Definitions for fiber bundle
fiber bun·dle

Princeton's WordNetRate this definition:0.0 / 0 votes

1. fiber bundle, fibre bundle, fascicle, fasciculusnoun

   a bundle of fibers (especially nerve fibers)

WiktionaryRate this definition:0.0 / 0 votes

1. fiber bundlenoun

   A topological space that, if one examines only a small part of it at a time, looks consistently like some product space

WikipediaRate this definition:0.0 / 0 votes

1. Fiber bundle

   In mathematics, and particularly topology, a fiber bundle (or, in Commonwealth English: fibre bundle) is a space that is locally a product space, but globally may have a different topological structure. Specifically, the similarity between a space E {\displaystyle E} and a product space B × F {\displaystyle B\times F} is defined using a continuous surjective map, π : E → B , {\displaystyle \pi :E\to B,} that in small regions of E {\displaystyle E} behaves just like a projection from corresponding regions of B × F {\displaystyle B\times F} to B . {\displaystyle B.} The map π , {\displaystyle \pi ,} called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space E {\displaystyle E} is known as the total space of the fiber bundle, B {\displaystyle B} as the base space, and F {\displaystyle F} the fiber. In the trivial case, E {\displaystyle E} is just B × F , {\displaystyle B\times F,} and the map π {\displaystyle \pi } is just the projection from the product space to the first factor. This is called a trivial bundle. Examples of non-trivial fiber bundles include the Möbius strip and Klein bottle, as well as nontrivial covering spaces. Fiber bundles, such as the tangent bundle of a manifold and other more general vector bundles, play an important role in differential geometry and differential topology, as do principal bundles. Mappings between total spaces of fiber bundles that "commute" with the projection maps are known as bundle maps, and the class of fiber bundles forms a category with respect to such mappings. A bundle map from the base space itself (with the identity mapping as projection) to E {\displaystyle E} is called a section of E . {\displaystyle E.} Fiber bundles can be specialized in a number of ways, the most common of which is requiring that the transition maps between the local trivial patches lie in a certain topological group, known as the structure group, acting on the fiber F {\displaystyle F} .

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1. fiber bundle

   A fiber bundle is a topological construct defined as a triple (E, B, F), where E is the total space, B is the base space, and F is the fiber. Additionally, there exists a continuous function π : E → B (known as the projection or submersion map) that locally, on a neighborhood of every point in E, provides a one-to-one correspondence with the product space B × F. Essentially, this means the structure of the bundle near any given point looks like the direct product of B and F, but globally this structure may be more complex. Common examples of fiber bundles include the tangent bundle and the Möbius strip.

WikidataRate this definition:0.0 / 0 votes

1. Fiber bundle

   In mathematics, and particularly topology, a fiber bundle is intuitively a space which locally "looks" like a certain product space, but globally may have a different topological structure. Specifically, the similarity between the fiber bundle E and a product space B × F is defined using a continuous surjective map that in small regions of E behaves just like a projection from corresponding regions of B × F to B. The map π, called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space E is known as the total space of the fiber bundle, B as the base space, and F the fiber. In the trivial case, E is just B × F, and the map π is just the projection from the product space to the first factor. This is called a trivial bundle. Examples of non-trivial fiber bundles, that is, bundles twisted in the large, include the Möbius strip and Klein bottle, as well as nontrivial covering spaces. Fiber bundles such as the tangent bundle of a manifold and more general vector bundles play an important role in differential geometry and differential topology, as do principal bundles. Mappings which factor over the projection map are known as bundle maps, and the set of fiber bundles forms a category with respect to such mappings. A bundle map from the base space itself to E is called a section of E. Fiber bundles can be generalized in a number of ways, the most common of which is requiring that the transition between the local trivial patches should lie in a certain topological group, known as the structure group, acting on the fiber F.

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1. • Nervous Tissue

Anagrams for fiber bundle »

1. fibre bundle

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Numerology

1. Chaldean Numerology

   The numerical value of fiber bundle in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of fiber bundle in Pythagorean Numerology is: 8

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=fiber bundle
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Fiber_Bundle
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Fiber_Bundle
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=fiber bundle