Skip to main content

On the Proof that Compact Hausdorff Boolean Algebras are Powersets

Abstract

Papert Strauss (Proc. London Math. Soc. 18(3), 217–230, 1968) used Pontryagin duality to prove that a compact Hausdorff topological Boolean algebra is a powerset algebra. We give a more elementary proof of this result that relies on a version of Bogolyubov’s lemma.

This is a preview of subscription content, access via your institution.

References

  1. Anderson, L.W.: One dimensional topological lattices. Proc. Amer. Math. Soc. 10, 715–720 (1959)

    MathSciNet  Article  MATH  Google Scholar 

  2. Dikranjan, D.N., Prodanov, I.R., Stoyanov, L.N.: Topological groups. Characters, dualities and minimal group topologies. Monographs and Textbooks in Pure and Applied Mathematics, vol. 130. Marcel Dekker, Inc., New York (1990)

    Google Scholar 

  3. Dikranjan, D.N., Stoyanov, L.N.: An elementary approach to Haar integration and Pontryagin duality in locally compact abelian groups. Topology Appl. 158(15), 1942–1961 (2011)

    MathSciNet  Article  MATH  Google Scholar 

  4. Johnstone, P.T.: Stone spaces. Cambridge University Press, Cambridge (1982)

    MATH  Google Scholar 

  5. Papert Strauss, D.: Topological lattices. Proc. London Math. Soc. 18(3), 217–230 (1968)

    MathSciNet  Article  MATH  Google Scholar 

  6. Prodanov, I.R.: Elementary proof of the Peter-Weyl theorem. C. R. Acad. Bulgare Sci. 34(3), 315–318 (1981). (Russian)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guram Bezhanishvili.

Additional information

To the memory of Dito Pataraia (1963–2011)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bezhanishvili, G., Harding, J. On the Proof that Compact Hausdorff Boolean Algebras are Powersets. Order 33, 263–268 (2016). https://doi.org/10.1007/s11083-015-9363-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11083-015-9363-y

Keywords

  • Topological boolean algebra
  • Pontryagin duality
  • Bogolyubov’s lemma