Inverse limits with set-valued functions having graphs that are arcs (Q2042100)

\textit{I. Banič} and \textit{J. Kennedy} [Topology Appl. 190, 9--21 (2015; Zbl 1321.54045)] have drawn attention to a natural but largely unexplored field of study in the theory of inverse limits with set-valued functions. They considered connectivity questions in inverse limits on \([0, 1]\) with a single set-valued bonding function whose graph is an arc. Their paper is perhaps the first in the literature to concentrate on this particular class of set-valued bonding functions. At the end of that paper, they asked whether an inverse limit on \([0,1]\) is connected in case there is a single bonding function having a graph that is an arc and \(G(f^n)\) is connected for each \(n\). In the present paper the author provides a negative answer to that question, includes some additional examples as well as a theorem on trivial shape (not requiring that the graphs be arcs), and poses several questions concerning, for the most part, inverse limits with set-valued functions whose graphs are arcs.