Open problems in continuum theory problem 24

Problem 24 (OPICT): Let $X$ be an atriodic absolute retract for hereditarily unicoherent continua. Must $X$ be the inverse limit of arcs with open bonding mappings?

Answer: Such a continuum $X$ must be an indecomposable, arc-like, Kelley continuum with only arcs for proper subcontinua.

J. J. Charatonik, W. J. Charatonik and J. R. Prajs, Atriodic absolute retracts for hereditarily unicoherent continua, Houston J. Math. 30 (2004), 1069 - 1087

J. J. Charatonik and J. R. Prajs, Generalized ε-push property for certain atriodic continua, Houston J. Math. 31 (2005), 441-450.