Geodesic
Structure spaces for rings of continuous functions with applications to realcompactifications
Fundamenta Mathematicae, Tome 152 (1997) no. 2, pp. 151-163

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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).
DOI : 10.4064/fm-152-2-151-163
Keywords: ring of continuous functions, maximal ideal, ultrafilter, realcompactification

Lothar Redlin 1 ; Saleem Watson 1

1 
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Lothar Redlin; Saleem Watson. Structure spaces for rings of continuous functions with applications to realcompactifications. Fundamenta Mathematicae, Tome 152 (1997) no. 2, pp. 151-163. doi: 10.4064/fm-152-2-151-163

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