We identify all uniform limits of polynomials on the closed unit disc with respect to the chordal metric \c{ hi} . One such limit is f=oo. The other limits are holomorphic functions f:-->C so that for every { \zeta} in the boundary of unit disc D the limf(z) while z-->{ \zeta} exists in C U { oo}. The class of the above functions is denoted by A(D)~. We study properties of the members of A(D)~, as well as, some topological properties of A(D)~ endowed with its natural metric topology. There are several open questions and new directions of investigation.
Categories: math.CV