Remark on a Theorem of A. Atzmon Regarding Uniform Approximation

We prove a completeness result for the Euclidean space ℝ^d which was proved earlier for the case d=1. This result uses the action of translation, dilation and rotation on a single function to yield dense subspace of C₀(ℝ^d), the Banach space of continuous functions on ℝ^d vanishing at infinity with supremum norm.