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Incomplete algebras

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

Abstract

The quotient of a Boolean algebra modulo an ideal may turn out to have a higher degree of completeness than one has a right to expect. Thus, for instance, the reduced Borel algebra and the reduced measure algebra of the unit interval are not only σ-algebras, which is all that the general theory can predict, but even complete. A few observations of this kind are likely to tip the balance of expectations too far over to the optimistic side. The purpose of this section is to provide a counterbalance in the form of some counterexamples. In other words, we shall obtain a few negative results: we shall see that certain quotient algebras are not complete.

Keywords

Boolean Algebra Measure Zero Unit Interval Continuum Hypothesis Quotient Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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