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A note on zero-sets in the Stone-Čech compactification

Published online by Cambridge University Press:  17 April 2009

D. Rudd
D. Rudd
Affiliation:
Department of Mathematics, Old Dominion University, Norfolk, Virginia, USA.
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Abstract

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The ring C(X) is the ring of all continuous real-valued functions on a completely regular Hausdorff space X, and βX is the Stone-Čech compactification of X.

The author proves a theorem which leads to a characterization of those zero-sets in X whose closures (in βX) are zero-sets in βX, and relates this characterization to the ideals in the ring C(X).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 2 , April 1975 , pp. 227 - 230
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Gillman, Leonard and Jerison, Meyer, Rings of continuous functions (Van Nostrand, Princeton, New Jersey; Toronto; London; New York; 1960).CrossRefGoogle Scholar
[2]Rudd, David, “On isomorphisms between ideals in rings of continuous functions”, Trans. Amer. Math. Soc. 159 (1971), 335–353.CrossRefGoogle Scholar