On structure spaces of ideals in rings of continuous functions

Rudd, David

doi:10.1090/S0002-9947-1974-0350690-6

On structure spaces of ideals in rings of continuous functions
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Trans. Amer. Math. Soc. 190 (1974), 393-403 Request permission

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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