A problem in plane topology

In a closed and bounded region of the plane there is given a field of curves satisfying natural continuity properties expressed in geometrical terms. We show that such a field is easy to construct: the ends of all curves which separate the region lie on its boundary.Translated from Matematicheskie Zametki, Vol. 5, No. 6, pp. 709–718, June, 1969.The author wishes to thank his scientific advisor S. G. Krein.