Menger's theorem for countable graphs

Abstract The countable case of a conjecture of Erdos is settled: let G = (V, E) be a directed or undirected graph, where V is countable, and let A, B⊆V. There exists then a set P of disjoint A − B paths and an A − B separating set S of vertices so that S consists of the choice of precisely one vertex from each path in P .