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).
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© 1974 Springer-Verlag New York Inc.
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Halmos, P.R. (1974). Duality for homomorphisms. In: Lectures on Boolean Algebras. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9855-7_20
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DOI: https://doi.org/10.1007/978-1-4612-9855-7_20
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90094-0
Online ISBN: 978-1-4612-9855-7
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