Isomorphisms of countable factors

  • Paul R. Halmos
Part of the Undergraduate Texts in Mathematics book series (UTM)


The purpose of this section is to show (following Hanf, as simplified, orally, by Dana Scott) that there exist countable Boolean algebras A and B such that A =A × B × B but AA × B. The method of attack is topological; in fact, we shall construct Boolean spaces X and Y, each with a countable base, so that X = X + Y + Y but XX + Y. (The equal sign denotes homeomorphism here.)


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Copyright information

© Springer-Verlag New York Inc. 1974

Authors and Affiliations

  • Paul R. Halmos
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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