| Popis: |
Banic and Kennedy (2015) [8] have drawn attention to a natural but largely unexplored field of study in the theory of inverse limits with set-valued functions, namely using bonding functions having graphs that are arcs. At the end of that paper they pose a question: If f : [ 0 , 1 ] → 2 [ 0 , 1 ] is an upper semi-continuous function such that G ( f n ) is connected for each n and G ( f ) is an arc, is lim ← f connected? In this paper we provide a negative answer to that question, include some additional examples as well as a theorem on trivial shape (not requiring that the graphs be arcs), and pose several questions concerning, for the most part, inverse limits with set-valued functions whose graphs are arcs. |
Full Text from ScienceDirect