LOCAL CONNECTEDNESS AND UNICOHERENCE AT SUBCONTINUA

Let X be a continuum and Y a subcontinuum of X. The purpose of this paper is to investigate the relation between the conditions \X is unicoherent at Y " and \Y is unicoherent". We say that X is strangled by Y if the closure of each component of X n Y intersects Y in one single point. We prove: If X is strangled by Y and Y is unicoherent then X is unicoherent at Y. We also prove the converse for a locally connected (not necessarily metric) continuum X.