Departamento de Matematicas, Faculdad de Ciencias, UNAM, Circuito exterior C.U. Mexico D.F.
Abstract. 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 \ 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.
1991 Mathematics Subject Classification. 54F20, 54F55.
Key words and phrases. Unicoherence, unicoherence at subcontinua, strangled, cyclic element, local connectedness, semilocal connectedness.