Structure spaces for rings of continuous functions with applications to realcompactifications

Tom 152 / 1997

, Fundamenta Mathematicae 152 (1997), 151-163 DOI: 10.4064/fm-152-2-151-163


Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).

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