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A characterization of boolean spaces

Published online by Cambridge University Press:  17 April 2009

C.E. Dickerson  and
M.E. Moore
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Abstract

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A boolean space is a compact Hausdorff space which is zero-dimensional. In this paper, a boolean space X is characterized in terms of its ring of real-valued functions C(X). The result is sharpened for the case when X is an F-space (every finitely generated ideal of C(X) is principal).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 89 - 93
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Gillman, Leonard and Henriksen, Melvin, “Rings of continuous functions in which every finitely generated ideal is principal”, Trans. Amer. Math. Soc. 82 (1956), 366–391.CrossRefGoogle Scholar
[2]Gillman, Leonard and Jerison, Meyer, Rings of continuous functions (Van Nostrand, Princeton, New Jersey; Toronto; London; New York; 1960).CrossRefGoogle Scholar
[3]Halmos, Paul R., Lectures on Boolean algebras (Van Nostrand, Princeton, New Jersey; Toronto; New York; London; 1963).Google Scholar
[4]Moore, Marion and Steger, Arthur, “Some results on completability in commutative rings”, Pacific J. Math. 37 (1971), 453–460.CrossRefGoogle Scholar
[5]Pierce, R.S., Compact zero-dimensional metric spaces of finite type (Mem. Amer. Math. Soc., 130. Amer. Math. Soc., Providence, Rhode Island, 1972).CrossRefGoogle Scholar
[6]Sikorski, Roman, Boolean algebras, 2nd ed. (Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, 25. Springer-Verlag, Berlin, New York; Academic Press, New York; 1964).Google Scholar