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Pointwise Sequentially Closed Ideals in C*(X)

Published online by Cambridge University Press:  20 November 2018

Richard G. Wilson
Richard G. Wilson*
Affiliation:
Carleton University, Ottawa, Ontario
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The purpose of this paper is to determine the conditions under which the maximal ideals of the ring C*(X)—the bounded real-valued continuous functions on a completely regular Hausdorff space X—are closed under pointwise convergence of sequences. Whereas the maximal ideals of C*(X) are closed under pointwise convergence of nets if and only if X is compact, it is shown that a necessary and sufficient condition for their pointwise sequential closure is that X be pseudocompact (i.e. that all real-valued continuous functions of X be bounded).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 115 - 117
Copyright
Copyright © Canadian Mathematical Society 1973

References

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