Structure spaces for rings of continuous functions with applications to realcompactifications
Volume 152 / 1997
Fundamenta Mathematicae 152 (1997), 151-163
DOI: 10.4064/fm-152-2-151-163
Abstract
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).
