FIBRE BUNDLE Meaning and
Definition
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A fibre bundle, in mathematics and specifically in differential geometry, is a mathematical object that intuitively represents properties of a space that vary smoothly from point to point. More formally, a fibre bundle consists of a total space, a base space, and a projection map. The total space is a collection of points that is the union of several smaller spaces, called fibres, which are all isomorphic to each other. The base space is a separate space that serves as a framework to which the fibres are attached. The projection map connects each point in the total space with a unique point in the base space.
Fibre bundles are often used to study and analyze tensors and manifolds. They can be classified based on the type of structure they possess, such as the dimensionality of the fibre and the base space. Some common examples of fibre bundles include line bundles, tangent bundles, and principal bundles.
The concept of fibre bundles enables the study of geometric and topological properties in a more flexible and general way. By examining the variations of properties within the fibres, mathematicians can gain insights into the behavior of systems across different scales. This versatile tool is fundamental in various branches of mathematics, including differential geometry, topology, and theoretical physics.
Common Misspellings for FIBRE BUNDLE
- dibre bundle
- cibre bundle
- vibre bundle
- gibre bundle
- tibre bundle
- ribre bundle
- fubre bundle
- fjbre bundle
- fkbre bundle
- fobre bundle
- f9bre bundle
- f8bre bundle
- fivre bundle
- finre bundle
- fihre bundle
- figre bundle
- fibde bundle
- fibfe bundle
- fibte bundle
Etymology of FIBRE BUNDLE
The word "Fibre Bundle" in mathematics is composed of two parts: "fibre" and "bundle".
The term "fibre" originated from the Latin word "fibra", meaning "thread" or "fiber". In the context of mathematics and topology, a fibre is a set of points that are structurally similar to each other. In a fibre bundle, each fibre is a small subspace that looks the same as every other fibre. A fibre typically corresponds to a copy of another mathematical object, such as a vector space or a topological space.
The term "bundle" in mathematics has its roots in the Old English word "byndele", meaning "a binding". The concept of bundling originated from examples such as bundles of hay or firewood, where multiple elements are bound or tied together.
Similar spelling word for FIBRE BUNDLE
