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On the Proof that Compact Hausdorff Boolean Algebras are Powersets


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.

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Correspondence to Guram Bezhanishvili.

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To the memory of Dito Pataraia (1963–2011)

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Bezhanishvili, G., Harding, J. On the Proof that Compact Hausdorff Boolean Algebras are Powersets. Order 33, 263–268 (2016).

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