Geodesic
Accumulation Points of Continuous Realvalued Functions and Compactifications
Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 47-52

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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. 
Choo, Eng Ung. Accumulation Points of Continuous Realvalued Functions and Compactifications. Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 47-52. doi: 10.4153/CMB-1977-009-7
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