Connectedness of inverse limits with functions f_i where either f_i or f_i~(-1) is a union of continuum-valued functions

摘要

We establish a general theorem for connectedness of the inverse limit X of an inverse sequence {X-i, f(i) }(i = 1) on metric continua with surjective upper semi-continuous set-valued bonding functions, where for each i = 1, f(i) has a connected graph, and either f(i) or f(i)(-1) is a union of continuum-valued functions. Properties of certain set-valued functions from the factor spaces onto partial graphs in the inverse sequence imply connectedness of X. (C) 2019 Elsevier B.V. All rights reserved.