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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 \(A(X)\subseteq C(X)\).

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