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Map of municipal broadband networks in the United States Cybertelecom: Municipal Broadband MuniWireless.com: the portal for the latest news and information about municipal wireless broadband projects around the world with a comprehensive summary of projects, market research reports, and conferences; set up by Esme Vos in 2003, updated list of U ...
Conversely, general bundle maps can be reduced to bundle maps over a fixed base space using the notion of a pullback bundle. If π F:F→ N is a fiber bundle over N and f:M→ N is a continuous map, then the pullback of F by f is a fiber bundle f * F over M whose fiber over x is given by (f * F) x = F f(x).
A bundle map from the base space itself (with the identity mapping as projection) to is called a section of . Fiber bundles can be specialized in a number of ways, the most common of which is requiring that the transition maps between the local trivial patches lie in a certain topological group, known as the structure group, acting on the fiber .
"fiber to the building Internet speeds of up to 500/50 Mbit/s to residential and business customers … The available fiber tiers are 100 Mbit/s ($95), 200 Mbit/s ($200), or 500 Mbit/s ($300)." [19] [20] Hotwire: Salisbury, NC: City network providing residential and business services including TV, phone, and Internet. LymeFiber Lyme, New Hampshire
Spread Networks is a company founded by Dan Spivey and backed by James L. Barksdale (former CEO of Netscape) that claims to offer Internet connectivity between Chicago and New York City at ultra-low latency (i.e. speeds that are very close to the speed of light), high bandwidth, and high reliability, using dark fiber.
A mapping : between total spaces of two fibrations : and : with the same base space is a fibration homomorphism if the following diagram commutes: . The mapping is a fiber homotopy equivalence if in addition a fibration homomorphism : exists, such that the mappings and are homotopic, by fibration homomorphisms, to the identities and . [2]: 405-406
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.
This projection maps each element of the tangent space to the single point . The tangent bundle comes equipped with a natural topology (described in a section below ). With this topology, the tangent bundle to a manifold is the prototypical example of a vector bundle (which is a fiber bundle whose fibers are vector spaces ).