Geometry VI pp 436-453 | Cite as

Vector Bundles

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


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.


Vector Bundle Topological Space Linear Space Tangent Bundle Smooth Manifold 
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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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