We derive approximation results for continuous functions from some Frechet space into its field. The approximation is similar to the well known universal approximation theorems for continuous functions defined on the real line or products thereof, where approximation is done with (multilayer) neural networks [Cybenko, 1989], [Hornik et. al., 1989], [Funahashi, 1989], [Leshno et. al., 1931]. Similar to classical neural networks, the approximating functions that we obtain are easy to implement and allow for fast computation and fitting. We show several possible applications of these results.