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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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