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Geometry VI pp 436-453 | Cite as

Vector Bundles

  • M. M. Postnikov
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 91)

Abstract

The word “bundle” recalls an association with a certain set ε divided into nonempty disjoint sets, the fibers. Let ε be the set of all fibers, and let π: ε → β be the mapping that sets the fiber containing a point pε in correspondence to this point. The mapping π is uniquely defined by the bundle and in turn uniquely defines this bundle. Moreover, any surjective mapping of the form π: ε → β yields a certain bundle of the set ε (consisting of the inverse images π-1(b) of points b ∈ β). Of course, in the topological case (where ε is a topological space), it is natural to assume that the mapping π is continuous. All this is an explanation and motivation for the following definition.

Keywords

Vector Bundle Topological Space Linear Space Tangent Bundle Smooth Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • M. M. Postnikov
    • 1
  1. 1.MIRANMoscowRussia

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