Rational approximation on $A^{\infty }(\varOmega )$

Abstract

Let $\{U_i\}_{i\in I}$ be a family of bounded planar domains in $\mathbb C$. Here $A(\prod_{i\in I}U_i)$ stands for the set of continuous functions on $\prod_{i\in I}\overline{U_i}$ endowed with the product topology that are separately holomorphic on each