Monotone and weakly confluent set-valued functions and their inverse limits

We use this to show two main results for inverse limits on [0,1]. First, if fj:[0,1]→2[0,1] is monotone for each j∈N, then lim←fj is locally connected. Second, if fj:[0,1]→2[0,1] is weakly confluent for each j∈N, we establish a sufficient condition for lim←fj to contain an indecomposable continuum.