The Inverse Limit Property for Subcontinua of Inverse Limits of Set-valued Functions - Kelly, James (Topology Proceedings, 2022)
We examine when a subcontinuum of an inverse limit with set-valued functions is equal to the inverse limit of its projections. There are multiple ways to interpret this problem. We focus on one particular interpretation due to Iztok Banić et al. [Bull. Malays. Math. Sci. Soc. 42 (2017), no. 3, 835-846]. When this does hold, we say that the inverse sequence has ILP(C(f_i)). We identify properties of the bonding functions which imply that the system has ILP(C(_i)). We also show a relationship between this property and connectedness im kleinen and use this to identify inverse sequences that do not have ILP(C(_⟵ )).