Unicoherence at subcontinua

AbstractThe notion of unicoherence at a subcontinuum of a metric continuum is defined, and relationships between this local form of unicoherence and certain existing forms of unicoherence are investigated. In particular, it is shown that strong unicoherence is equivalent to unicoherence at every subcontinuum and that weak hereditary unicoherence is equivalent to unicoherence at every subcontinuum having nonempty interior. Further, if every indecomposable subcontinuum of a continuum X has nonempty interior, then X is strongly unicoherent if and only if X is weakly hereditarily unicoherent. New characterizations of dendrites are obtained by requiring either aposyndesis or local connectivity and unicoherence at certain subcontinua