Finite Graphs and Inverse Limits with Set-Valued Functions on Intervals - Nall, Van; Vidal-Escobar, Ivon (Topology Proceedings, 2020)
If the inverse limit of upper semi-continuous set-valued functions from [0, 1] to the closed subsets of [0, 1] is a finite graph G, then for some N and all n ≥ N, the projection onto the first n coordinates of that inverse limit is a projection onto a finite graph that is homeomorphic to G.