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

Bors 

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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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