Conditions for chainability of inverse limits on [0,1] with interval-valued functions

Abstract

For an inverse sequence on [0,1] with interval-valued functions, we establish necessary conditions on the bonding functions for chainability of the inverse limit space. We also characterize chainability of the inverse limit in this setting in terms of properties of the bonding functions fi and the induced functions Fn:[0,1]→G′(f1,…,fn−1). The properties, in both cases, are related to how triods arise in the partial graphs associated with the inverse sequence when each graph G(fi) is chainable.