Adelic versions of the Weierstrass approximation theorem

Jean-Luc Chabert, Giulio Peruginelli

Let $\underline{E}={\prod }_{p\in \mathbb{P}}{E}_p$ be a compact subset of $\hat{\mathbb{Z}}={\prod }_{p\in \mathbb{P}}{\mathbb{Z}}_p$ and denote by $\mathcal C(\underline{E},\widehat{\mat…