Runge domain

Summary

A Runge domain is an open set in $\C^n$ on which every holomorphic function can be approximated by polynomials, uniformly on each compact subset. The name comes from Runge's theorem, which describes such open sets in the plane: they are the open sets whose connected components are simply connected. In several variables, convex domains and balls are Runge domains, and the Oka–Weil theorem is the main tool to recognise them.