On prime ends and local connectivity

Let U subset of (C) over cap be a simply connected domain whose complement K = (C) over cap backslash U contains more than one point. We show that the impression of a prime end of U contains at most two points at which K is locally connected. This is achieved by establishing a characterization of local connectivity of K at a point z(0) is an element of partial derivative U in terms of the prime ends of U whose impressions contain z(0), and then invoking a result of Ursell and Young.