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Structure spaces for rings of continuous functions with applications to realcompactifications. (English) Zbl 0877.54015
Let \(X\) be a completely regular space and \(C(X)\) the ring of continuous real-valued functions on \(X\). The authors define the notion of a subring \(A(X)\subseteq C(X)\) closed under local bounded inversion and show that the structure space of \(A(X)\) is a quotient of the Stone-Čech compactification \(\beta X\). This result is used to prove that any realcompactification of \(X\) is homeomorphic to a subspace of the structure space of some ring of continuous functions \(A(X)\subseteq C(X)\).

MSC:
54C40 Algebraic properties of function spaces in general topology
46E25 Rings and algebras of continuous, differentiable or analytic functions
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