Some Theorems on Inverse Limits with Monotone Upper Semi-continuous Bonding Functions - Oshima, Yoshiyuki (Topology Proceedings, 2022)
In [Duke Math. J. 21 (1954), pp. 233-245], C. E. Capel showed that local connectedness of factor spaces is inherited by the inverse limits with surjective monotone bonding maps. Also, in [Topology Appl. 285 (2020), 107393, 25 pp.], Benjamin Espinoza and Eiichi Matsuhashi showed that $n$-aposyndesis, semiaposyndesis, continuum-chainability, Wilderness, being $D$, being $D^*$, and co-local connectedness are preserved under inverse limits with surjective monotone bonding maps. On the other hand, in [Topology Appl. 228 (2017), pp. 486-500], James P. Kelly, showed that inverse limits of arcs with surjective monotone upper semicontinuous bonding functions are locally connected. In this paper, we investigate the set-valued versions of the above results by Espinoza and Matsuhashi.