Point separation by bounded analytic functions of a covering Riemann surface (Q1092278)

We consider a two sheeted, unlimited, covering Riemann surface of a Riemann surface. Results of both positive and negative directions on the point separation by bounded analytic functions of the covering Riemann surface are given when the points of the base Riemann surface are separated by bounded analytic functions. We investigate effects of a converging sequence of branching points in the case that the base Riemann surface is a plane domain. Also, we show that locations of (even a pair of) branching points become serious in the case of general Riemann surfaces.