Each archimedean l-group admits a unique essential closure, which is the l-group of continuous almost finite real-valued functions on some Stonean space; thus the l-group C ( X ) C(X) of real-valued continuous functions on a topological space X admits such an essential closure. In this note we will construct a natural embedding of C ( X ) C(X) into its essential closure, making explicit the topological relationship between X and the appropriate Stonean space.