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...

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)...

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...

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

the 3-sphere is composed of fibers, where each fiber is a circle — one for each point of the 2-sphere. This fiber bundle structure is denoted S 1 ↪ S...

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...

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...

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...

In mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered...

perspective of homotopy theory, a real line bundle therefore behaves much the same as a fiber bundle with a two-point fiber, that is, like a double cover. A special...

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...

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...

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...

A fiberscope is a flexible optical fiber bundle with an eyepiece on one end and a lens on the other that is used to examine and inspect small, difficult-to-reach...

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)...

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...

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...

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...

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...

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}...

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...

a manifold. As such, the fiber is a vector space and the tensor bundle is a special kind of vector bundle. The vector bundle is a natural idea of "vector...

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...

article by Tai Tsun Wu and C. N. Yang comparing electromagnetism and fiber bundle theory. This dictionary has been credited as bringing mathematics and...

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...

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...

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

tensor bundle a connection is needed, except for the special case of the exterior derivative of antisymmetric tensors. A tensor bundle is a fiber bundle where...