Monotone decompositions of IUC continua

Abstract

For the class of hereditarily unicoherent metric continua a spectrum of monotone decompositions has been developed by several authors which "improves" the quotient spaces. This spectrum is developed for a broader class of continua, namely continua with property IUC. A metric continuum M M has property IUC provided each proper subcontinuum of M M with interior is unicoherent. One important result which develops is that semiaposyndetic IUC continua are hereditarily arcwise connected. Also the notion of smoothness is studied for IUC continua.