Inverse limits of upper semicontinuous functions and indecomposable continua

摘要

We consider how inverse limits and Mahavier-products of upper semicontinuous functions relate to their bonding functions with respect to indecomposability and connectedness. We show that if such an inverse limit is decomposable then for some n, the Mahavier product of its first n bonding functions is decomposable. It was shown in [3] that if the graphs of bonding functions of a Mahavier-product or inverse limit are pseudoarcs then it is disconnected. We show that a Mahavier-product whose bonding functions have indecomposable graphs can be connected. We also show that the full projection property is not a necessary condition for an indecomposable inverse limit. (C) 2020 Elsevier B.V. All rights reserved.