DMS Set Theoretic Topology/Continuum Theory Seminar

Abstract: We prove that if \(X\) is an inverse limit of Hausdorff arcs and \(M \subset X\)  is a hereditarily indecomposable continuum, then \(M\) is a metric continuum.  We also provide an example to argue that, unlike in the metric situation, there exist continua which are inverse limits of Hausdorff arcs which cannot be embedded in the product of two Hausdorff arcs.  This implies that the inverse limit situation needs to be considered separately from products of two Hausdorff arcs.