Interval-expressed tree-like continua with the fixed point property - Marsh, M. M. (Topology Proceedings, 2020)
Let T be the class of tree-like continua that admit representations as inverse limits on [0,1] with surjective upper semicontinuous set-valued functions. We show (1) if XT with interval-valued bonding functions f_i, where there exists m≥ 1 such that, for each i≥ m, the graph of f_i^-1 contains the graph of an interval-valued function, then X has the fixed point property, and (2) if XT with set-valued bonding functions f_i, where for each i≥ 1, f_i^-1 is an interval-valued function, then X is a λ-dendroid. We also provide an example of an indecomposable, non-arclike continuum in T that has the fixed point property.