• Igor R. Shafarevich
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 11)


We now make further use of the notion of a family of vector spaces f: EX over a topological space X introduced at the end of § 5. A homomorphism φ: EE′ of a family f: EX into a family f′: E′ → X is a continuous map φ which takes the fibre f −1(x) into (f′)−1(x) and is linear on the fibre for each point xX. If φ defines an isomorphism of the fibres, then φ is called an isomorphism.


Vector Bundle Fibre Bundle Elliptic Operator Marked Point Division Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Igor R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of ScienceMoscowRussia

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