Finite graphs that are inverse limits with a set valued function on \([0,1]\). (Q549145)

An arc is the inverse limit of the diagonal in \([0,1] \times [0,1]\). This presents the only known example of a closed subset of \([0,1] \times [0,1]\) whose generalized inverse limit is a finite graph. \textit{A. Illanes} has shown that a simple closed curve is not the generalized inverse limit of a closed subset of \([0,1] \times [0,1]\) [Proc. Am. Math. 139, No. 8, 2987--2993 (2011; Zbl 1232.54030)]. In the paper under review, Nall shows that the only finite graphs that can be obtained as inverse limits with a simple surjective upper semi-continuous bonding function from \([0,1]\) to the nonempty closed subsets of \([0,1]\) are an arc or a simple triod. However, it is not known if there is such a simple triod.