The class S of functions under study in this paper was introduced by V. I. Smirnov in 1932. This class was subsequently investigated by various authors, a pertinent paper to the present wrork being that of Tumarkin and Havinson [2], who showed that a plane compact set of logarithmic capacity zero is 5-removable. Another important development, due to Yamashita [3], wras that the class 5 could be characterized as those analytic functions ƒ for which log+ |ƒ| has a quasi-bounded harmonic majorant.

In what follows, we discuss the Smirnov class in the context of planar surfaces, exploiting some ideas in the work of Hejhal [1] to establish that a closed, bounded, totally disconnected set is S-removable if and only if its complement belongs to the null class Os.