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Foundational Material

  • Jürgen Jost
Chapter
  • 630 Downloads
Part of the Universitext book series (UTX)

Abstract

A topological space is a set M together with a family O of subsets of M satisfying the following properties:
  1. (i)
    $${\Omega _1},{\Omega _2} \in O \Rightarrow {\Omega _1} \cap {\Omega _2} \in O$$
     
  2. (ii)

    For any index set A: {\left( {{\Omega _\alpha }} \right)_{\alpha \in A}} \subset O \Rightarrow \bigcup\limits_{\alpha \in A} {{\Omega _a} \in O}

     
  3. (iii)
    $${\Omega _1},{\Omega _2} \in O \Rightarrow {\Omega _1} \cap {\Omega _2} \in O$$
     

Keywords

Vector Field Riemannian Manifold Vector Bundle Tangent Bundle Spin Structure 
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 2002

Authors and Affiliations

  • Jürgen Jost
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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