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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Closed ideals in $ C(X)$


Authors: Philip Nanzetta and Donald Plank
Journal: Proc. Amer. Math. Soc. 35 (1972), 601-606
MSC: Primary 54C40
DOI: https://doi.org/10.1090/S0002-9939-1972-0303496-1
MathSciNet review: 0303496
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Abstract: The characterization of uniformly closed ideals in $ C(X)$, for X compact Hausdorff, is well known. In this note, we extend this characterization to an arbitrary completely regular Hausdorff X and derive some corollaries.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0303496-1
Keywords: Rings of continuous functions, closed ideal, uniform topology, stationary set, extended real-valued function
Article copyright: © Copyright 1972 American Mathematical Society