Extending local homotopy equivalences

  • Martin Fuchs


We give an elementary proof of one of tom Dieck’s theorems. The theorem says that iff:X → Y is a local homotopy equivalence in a strong enough sense, thenf is a homotopy equivalence globally. Applications, 1. The base space of any numerable principalG-bundle is of the sme homotopy type as the Borel space of the bundle. 2. The nerve of a numerable coveringU ofX for which all finite intersections are contractible is of the same homotopy type asX.


Topological Space Base Space Homotopy Type Homotopy Theory Formal Covering 
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Copyright information

© Springer 1983

Authors and Affiliations

  • Martin Fuchs
    • 1
    • 2
  1. 1.Institut für Mathematik UniversitätKonstanzGermania dell'Ovest
  2. 2.Department of MathematicsMichigan State UniversityLansingU. S. A.

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