Let $\sigma : \mathbb{R} \to \mathbb{R}$ be a continuous, non-polynomial activation function. Let $\mathcal{N}^{\sigma}_{m,n}$ denote the class of feedforward neural networks with activation $\sigma$, $m$ input neurons, $n$ output neurons, and one hidden layer of arbitrary width. Let $K \subset \mathbb{R}^m$ be compact. Then $\mathcal{N}^{\sigma}_{m,n}$ is dense in $C(K, \mathbb{R}^n)$ with respect to the uniform norm.