Prime end

Summary

Prime ends are the ideal boundary points of a simply connected plane domain, introduced by Constantin Carathéodory. A prime end is described by a shrinking sequence of cross cuts that close in on the boundary. For a bounded simply connected domain, a conformal map from the unit disc matches the points of the unit circle with the prime ends. They are the right notion of boundary when the topological boundary is too irregular for the conformal map to extend continuously.