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.
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Anderson, L.W.: One dimensional topological lattices. Proc. Amer. Math. Soc. 10, 715–720 (1959)
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)
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)
Johnstone, P.T.: Stone spaces. Cambridge University Press, Cambridge (1982)
Papert Strauss, D.: Topological lattices. Proc. London Math. Soc. 18(3), 217–230 (1968)
Prodanov, I.R.: Elementary proof of the Peter-Weyl theorem. C. R. Acad. Bulgare Sci. 34(3), 315–318 (1981). (Russian)
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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). https://doi.org/10.1007/s11083-015-9363-y
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DOI: https://doi.org/10.1007/s11083-015-9363-y