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Published online by Cambridge University Press: 20 November 2018
All topological spaces are assumed to be completely regular. C(X) (resp. C*(X)) will denote the ring of all (resp. all bounded) continuous real-valued functions on X. βX is the Stone-Cech compactification of X. A real number t is said to be an accumulation point of a function f ∊ C(X) if and only if f-1[[t-ε, t + ε]] is not compact for every ε > 0.