Dimension and superposition of bounded continuous functions on locally compact, separable metric spaces

AbstractLet n be an integer with n ≥ 1 and X be an n-dimensional, locally compact, separable, metric space. Then there are 2n + 1 continuous real-valued functions φ1,..., φ2n+1 of X such that each bounded, continuous, real-valued function ƒ of X is representable in the form ƒ(x) = Σ2n+1i = 1 gi(φi(x)), x ∈ X, where g i ∈ C(R), i = 1,..., 2n+1. This gives a solution to a problem of Sternfeld