Decomposition spectra of rings of continuous functions

Abstract

Let S be a subset of a completely regular Hausdorff space X. Sufficient conditions on S and X are obtained for the ring of continuous real-valued functions on 5 to be isomorphic to an inverse limit of quotient rings of the ring of continuous functions on X, or, alternatively, of the ring of bounded continuous functions on X. An application to the theory of rings of quotients of rings of continuous functions is given.