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Duality for homomorphisms

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

Abstract

To establish a dual correspondence between structure-preserving mappings of Boolean algebras and Boolean spaces, it is best not to give preferential treatment either. A good way to stay neutral is to use the concept of pairing introduced in §18. Suppose, accordingly, that A is a Boolean algebra and X is a Boolean space, and suppose that 〈p, x〉 represents all continuous 2-valued functions on X and all 2-valued homomorphisms on A. Suppose, moreover, that B and Y are a similarly paired pair. The purpose of this section is to make a connection between continuous mappings (from X into Y) and homomorphisms (from B into A).

Keywords

Boolean Algebra Clopen Subset Dual Algebra Boolean Space Cantor Space 
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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