Skip to main content
SpringerLink
Log in

Extending local homotopy equivalences

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Brown R.,Elements of Modern Topology, Mc Graw-Hill, London (1968).

    MATH  Google Scholar 

  2. Dold A.,Partitions of unity in the theory of fibrations, Ann. of Math.78 (1963), 223–255.

    Article  MathSciNet  Google Scholar 

  3. Hu S. T.,Homotopy theory, Academic Press, New York (1959).

    MATH  Google Scholar 

  4. Puppe D.,Homotopiemengen und ihre induzierten Abbildungen I, Math. Z.69 (1958), 299–344.

    Article  MathSciNet  Google Scholar 

  5. Segal G. B.,Classifying spaces and spectral sequences, I.H.E.S. Pub. Math.34 (1968), 105–112.

    MATH  Google Scholar 

  6. Tom Dieck T.,Partitions of unity in homotopy theory, Comp. Math.23 (1971), 159–167.

    MATH  MathSciNet  Google Scholar 

  7. Vogt R. M.,Homotopy limits and colimits, Math.2 (1973) 134, 11–52.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik Universität, Konstanz, Germania dell'Ovest

    Martin Fuchs

  2. Department of Mathematics, Michigan State University, 48824, Lansing, Michigan, U. S. A.

    Martin Fuchs

Authors
  1. Martin Fuchs
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fuchs, M. Extending local homotopy equivalences. Rend. Circ. Mat. Palermo 32, 217–223 (1983). https://doi.org/10.1007/BF02844832

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02844832

Keywords

Search

Navigation