Regular open sets

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


The purpose of this section is to discuss one more example of a Boolean algebra. This example, the most intricate of all the ones so far, is one in which the elements of the Boolean algebra are subsets of a set, but the operations are not the usual set-theoretic ones, so that the Boolean algebra is not a field of sets. Artificial examples of this kind are not hard to manufacture; the example that follows arises rather naturally and plays an important role in the general theory of Boolean algebras.


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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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