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  2. Fiber (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Fiber_(mathematics)

    Fiber (mathematics) In mathematics, the fiber ( US English) or fibre ( British English) of an element under a function is the preimage of the singleton set , [1] : p.69 that is. As an example of abuse of notation, this set is often denoted as , which is technically incorrect since the inverse relation of is not necessarily a function.

  3. Fibre-optic Link Around the Globe - Wikipedia

    en.wikipedia.org/wiki/Fibre-optic_Link_Around...

    Fibre-optic Link Around the Globe ( FLAG) is a 28,000-kilometre-long (17,398 mi; 15,119 nmi) fibre optic mostly- submarine communications cable that connects the United Kingdom, Japan, India, and many places in between. The cable is operated by Global Cloud Xchange, a subsidiary of RCOM. [1] The system runs from the eastern coast of North ...

  4. Fibration - Wikipedia

    en.wikipedia.org/wiki/Fibration

    Fibration. A fibration (also called Hurewicz fibration) is a mapping satisfying the homotopy lifting property for all spaces The space is called base space and the space is called total space. The fiber over is the subspace [1] : 66.

  5. Fiber bundle - Wikipedia

    en.wikipedia.org/wiki/Fiber_bundle

    1) that, in analogy with a short exact sequence , indicates which space is the fiber, total space and base space, as well as the map from total to base space. A smooth fiber bundle is a fiber bundle in the category of smooth manifolds . That is, E , B , {\displaystyle E,B,} and F {\displaystyle F} are required to be smooth manifolds and all the functions above are required to be smooth maps ...

  6. Fiber to the premises in the United States - Wikipedia

    en.wikipedia.org/wiki/Fiber_to_the_premises_in...

    South-Southwest United States. With its U-verse product, AT&T (formerly SBC) had pursued a strategy of Fiber to the Neighborhood (FTTN) and had even delivered Fiber to the Premises (FTTP) prior to the services' launch. Currently, U-verse is deployed as a Fiber to the Hub (FTTH) service; the line connecting the hub to the home is a dual copper ...

  7. Pullback (category theory) - Wikipedia

    en.wikipedia.org/wiki/Pullback_(category_theory)

    Fiber bundles. 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 ...

  8. Bundle map - Wikipedia

    en.wikipedia.org/wiki/Bundle_map

    Bundle map. In mathematics, 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, depending on whether the fiber bundles in question have a common base space. There are also several variations on the basic theme, depending on precisely which category ...

  9. Homotopy fiber - Wikipedia

    en.wikipedia.org/wiki/Homotopy_fiber

    Homotopy fiber. In mathematics, especially homotopy theory, the homotopy fiber (sometimes called the mapping fiber) [1] is part of a construction that associates a fibration to an arbitrary continuous function of topological spaces . It acts as a homotopy theoretic kernel of a mapping of topological spaces due to the fact it yields a long exact ...

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