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In other words, is fiber-preserving, and f is the induced map on the space of fibers of E: since π E is surjective, f is uniquely determined by . For a given f , such a bundle map φ {\displaystyle \varphi } is said to be a bundle map covering f .
In summary, there is a one-to-one correspondence (up to equivalence) between the descents of principal connections to associated fiber bundles, and G-connections on associated fiber bundles. For this reason, in the category of fiber bundles with a structure group G , the principal connection contains all relevant information for G -connections ...
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Another example of a pullback comes from the theory of fiber bundles: given a bundle map π : E → B and a continuous map f : X → B, the pullback (formed in the category of topological spaces with continuous maps) X × B E is a fiber bundle over X called the pullback bundle. The associated commutative diagram is a morphism of fiber bundles.
In mathematics, a pullback bundle or induced bundle [1] [2] [3] is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B and a continuous map f : B′ → B one can define a "pullback" of E by f as a bundle f * E over B′. The fiber of f * E over a point b′ in B′ is just the fiber of E over f(b′).
Fiber Distributed Data Interface (FDDI) is a standard for data transmission in a local area network. It uses optical fiber as its standard underlying physical medium. It was also later specified to use copper cable, in which case it may be called CDDI (Copper Distributed Data Interface), standardized as TP-PMD (Twisted-Pair Physical Medium ...
The language of fibre bundles allows this notion of a section to be generalized to the case when is not necessarily a Cartesian product. If π : E → B {\displaystyle \pi \colon E\to B} is a fibre bundle, then a section is a choice of point σ ( x ) {\displaystyle \sigma (x)} in each of the fibres.
Diagram originally published by the Fiber Optics LAN Section of the Telecommunications Industry Association. Fiber to the Edge (FTTE), fiber to the telecom enclosure (FTTTE) or fiber to the zone (FTTZ), [1] is a fiber to the x networking approach used in the enterprise building (hotels, convention centers, office buildings, hospitals, senior living communities, Multi-Dwelling Units, stadiums ...