An extension of the disc algebra, II

Abstract

We identify the complex plane with the open unit disc by the homeomorphism. This leads to a compactification of, homeomorphic to. The Euclidean metric on induces a metric on. We identify all uniform limits of polynomials on with respect to the metric. The class of the above limits is an extension of the disc algebra and it is denoted by. We study properties of the elements of and topological properties of the class endowed with its natural topology. The class is different and, from the geometric point of view, richer than the class introduced, on the basis of the chordal metric. © 2013 Taylor & Francis.