In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally...

the mathematical field of topology, a section (or cross section) of a fiber bundle E {\displaystyle E} is a continuous right inverse of the projection function...

A principal G {\displaystyle G} -bundle, where G {\displaystyle G} denotes any topological group, is a fiber bundle π : P → X {\displaystyle \pi :P\to...

its optical waveguide properties. Individual coated fibers (or fibers formed into ribbons or bundles) then have a tough resin buffer layer or core tube(s)...

theory of fiber bundles with a structure group G {\displaystyle G} (a topological group) allows an operation of creating an associated bundle, in which...

Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Technically, Hopf found a many-to-one continuous function (or "map")...

In mathematics, a bundle is a generalization of a fiber bundle dropping the condition of a local product structure. The requirement of a local product...

mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B and a continuous...

3 to 0.5 mm. Each fiber bundle has a low density core region not occupied by fibers. The stress-strain response of the fiber bundles is nearly linear elastic...

its tangent bundle is trivial. Vector bundles are almost always required to be locally trivial, which means they are examples of fiber bundles. Also, the...

engineering) Fiber bundle, a topological space that looks locally like a product space Optical fiber bundle, a cable consisting of a collection of fiber optics...

sense on any smooth fiber bundle. In particular, it does not rely on the possible vector bundle structure of the underlying fiber bundle, but nevertheless...

a frame bundle is a principal fiber bundle F ( E ) {\displaystyle F(E)} associated with any vector bundle E {\displaystyle E} . The fiber of F ( E )...

each fiber, we get a line bundle on P ( V ) {\displaystyle \mathbf {P} (V)} . This line bundle is called the tautological line bundle. This line bundle is...

A fiberscope is a flexible optical fiber bundle with a lens on one end and an eyepiece or camera on the other. It is used to examine and inspect small...

maps) X ×B E is a fiber bundle over X called the pullback bundle. The associated commutative diagram is a morphism of fiber bundles. This is also the...

wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. Specially designed fibers are also...

a bundle map (or bundle morphism) is a morphism in the category of fiber bundles. There are two distinct, but closely related, notions of bundle map...

differential topology, the jet bundle is a certain construction that makes a new smooth fiber bundle out of a given smooth fiber bundle. It makes it possible to...

semicontinuous bundles of fibers or staple fibers. Machining of staple fibers can produce semicontinuous bundles of fibers down to 10 μm. Improving staple fiber manufacturing...

manifold) Connection (principal bundle) Connection (vector bundle) Connection (affine bundle) Connection (composite bundle) Connection (algebraic framework)...

to a manifold is the prototypical example of a vector bundle (which is a fiber bundle whose fibers are vector spaces). A section of T M {\displaystyle TM}...

In that example, the base space of a fiber bundle is pulled back, in the sense of precomposition, above. The fibers then travel along with the points in...

connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby...

fibers come from the phloem tissue of the plant. The other fiber crop fibers are hard/leaf fibers (come from the entirety of plant vascular bundles)...

In mathematics, the fiber bundle construction theorem is a theorem which constructs a fiber bundle from a given base space, fiber and a suitable set of...

manifolds and fiber bundles are partial functions. In the case of manifolds, the domain is the point set of the manifold. In the case of fiber bundles, the domain...

functions from M to T. (More generally, we can have smooth sections of a fiber bundle over M.) Examples of this M in physics include: In classical mechanics...

space and time. (In mathematical terms, the theory involves a fiber bundle in which the fiber at each point of the base space consists of possible coordinate...

fiber space is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a S 1 {\displaystyle S^{1}} -bundle (circle...