2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59952Theorem converse to Jordan's curve theorem says that {\it if a compact set $K$ has two complementary domains in $R^{2}$, from each of which it is at every point accessible, it is a simple closed curve}. We show that the requirement of this theorem that {\it all} points of $K$ were accessible from {\it both} complementary domains is surplus and prove one generalization of this theorem.Geometric TopologyGeneral Topology14E35; 57M50; 57N35text