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bundle of linear spaces

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  • 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.… …   Wikipedia

  • Double tangent bundle — In mathematics, particularly differential topology, the double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM,M) of a smooth manifold M [1]. The second… …   Wikipedia

  • Vector bundle — The Möbius strip is a line bundle over the 1 sphere S1. Locally around every point in S1, it looks like U × R, but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a… …   Wikipedia

  • Banach bundle — In mathematics, a Banach bundle is a vector bundle each of whose fibres is a Banach space, i.e. a complete normed vector space, possibly of infinite dimension.Definition of a Banach bundleLet M be a Banach manifold of class C p with p ≥ 0, called …   Wikipedia

  • Principal bundle — In mathematics, a principal bundle is a mathematical object which formalizes some of the essential features of a Cartesian product X times; G of a space X with a group G . Analogous to the Cartesian product, a principal bundle P is equipped with… …   Wikipedia

  • Fiber bundle — In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which looks locally like a product space. It may have a different global topological structure in that the space as a whole may not be homeomorphic to a… …   Wikipedia

  • Tangent bundle — In mathematics, the tangent bundle of a smooth (or differentiable) manifold M , denoted by T ( M ) or just TM , is the disjoint unionThe disjoint union assures that for any two points x 1 and x 2 of manifold M the tangent spaces T 1 and T 2 have… …   Wikipedia

  • Ample line bundle — In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold M into projective space. An ample line bundle is one such that some positive power is very ample. Globally… …   Wikipedia

  • Associated bundle — In mathematics, the theory of fiber bundles with a structure group G (a topological group) allows an operation of creating an associated bundle, in which the typical fiber of a bundle changes from F 1 to F 2, which are both topological spaces… …   Wikipedia

  • Tautological bundle — In mathematics, tautological bundle is a term for a particularly natural vector bundle occurring over a Grassmannian, and more specially over projective space. Canonical bundle as a name dropped out of favour, on the grounds that canonical is… …   Wikipedia

  • Differentiation in Fréchet spaces — In mathematics, in particular in functional analysis and nonlinear analysis, it is possible to define the derivative of a function between two Fréchet spaces. This notion of differentiation is significantly weaker than the derivative in a Banach… …   Wikipedia

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