A Note on Rational Approximation with Respect to Metrizable Compactifications of the Plane

Abstract

In the present note we examine possible extensions of Runge, Mergelyan and Arakelian Theorems, when the uniform approximation is meant with respect to the metric ρ of a metrizable compactification (S, ρ) of the complex plane C.

Keywords

• compactification
• Arakelian’s theorem
• Mergelyan’s theorem
• Runge’s theorem
• uniform approximation in the complex domain.