Some mapping characterizations of unicoherence
We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as...
We prove that a k-dimensional hereditarily indecomposable metrisable continuum is not a -valued absolute retract. We deduce from this that none of the classical characterizations of ANR (metric) extends to the class of stratifiable spaces.