Abstract
This chapter is intended mainly as an introduction for the reader who is not already familar with Boolean algebras. The central result is Stone’s Representation Theorem which shows that any Boolean algebra can be identified with the family of clopen subsets of some totally disconnected compact space. The reader who is familar with the relationships between Boolean algebras and totally disconnected compact spaces will probably wish to omit this chapter and perhaps return to specific topics within the chapter as they are used later. The material on separability will be used in connection with βℕ\ℕ in Chapters 3 and 7. The homomorphism described in Proposition 2.16 will be used in Chapter 3 to relate ℕ to βℕ\ℕ. The only occasion in this chapter where the Stone-Čech compactification plays an important part is in Examples 2.14 and 2.15 which are based on properties of βℚ. Propositions 2.3 and 2.5 together with the Stone Representation Theorem will be needed in Chapter 10 in the context of projectives.
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© 1974 Springer-Verlag Berlin Heidelberg New York
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Walker, R.C. (1974). Boolean Algebras. In: Walker, R.C. (eds) The Stone-Čech Compactification. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61935-9_2
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DOI: https://doi.org/10.1007/978-3-642-61935-9_2
Publisher Name: Springer, Berlin, Heidelberg
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