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A note on the intersection of free maximal ideals

Published online by Cambridge University Press:  09 April 2009

Stewart M. Robinson
Stewart M. Robinson
Affiliation:
The Cleveland State University
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In [2] we proved that if X admits a complete uniform structure, the intersection of the free maximal ideals in C(x) is precisely Ck(X), the ring of functions with compact support. In the present paper we are able to sharpen this result somewhat and give necessary and sufficient conditions on a space X so that this conclusion holds. Both our previous result and that of Kohls for p-spaces follow as special cases of our theorem.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 1-2 , August 1969 , pp. 204 - 206
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Gillman, L. and Jerison, M., Rings of Continuous Functions, (Van Nostrand Co., Princeton, New Jersey, 1960).Google Scholar
[2]Robinson, S. M., ‘The intersection of the free maximal ideals in a complete space’, Proceedings of the American Mathematical Society, 17, 04 1966, pp. 468–469.CrossRefGoogle Scholar