INDECOMPOSABLE INVERSE LIMITS ON GRAPHS

Abstract

We obtain results, involving easily observable properties of bonding mappings, that ensure indecomposability of inverse limits on graphs. An allowable collection of $n$ arcs in a graph is defined, and two related properties of collections of arcs in a graph are introduced. In an inverse sequence on graphs, if compositions of the bonding mappings are $n$-pass maps on certain allowable collections of $n$ arcs, then the inverse limit space will be indecomposable. We provide examples that illustrate the use of our results.