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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On structure spaces of ideals in rings of continuous functions


Author: David Rudd
Journal: Trans. Amer. Math. Soc. 190 (1974), 393-403
MSC: Primary 54C40; Secondary 46E25
DOI: https://doi.org/10.1090/S0002-9947-1974-0350690-6
MathSciNet review: 0350690
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Abstract: A ring of continuous functions is a ring of the form $ C(X)$, the ring of all continuous real-valued functions on a completely regular Hausdorff space X.

With each ideal I of $ C(X)$, we associate certain subalgebras of $ C(X)$, and discuss their structure spaces.

We give necessary and sufficient conditions for two ideals in rings of continuous functions to have homeomorphic structure spaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0350690-6
Keywords: Rings of real-valued continuous functions, ideals, structure spaces, uniform closure
Article copyright: © Copyright 1974 American Mathematical Society

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