Abstract
In this paper, we investigate the inverse limits of two related parameterized families of upper semi-continuous set-valued functions. We include a theorem one consequence of which is that certain inverse limits with a single bonding function from one of these families are the closure of a topological ray (usually with indecomposable remainder). Also included is a theorem giving a new sufficient condition that an inverse limit with set-valued functions be an indecomposable continuum. It is shown that some, but not all, functions from these families produce chainable continua. This expands the list of examples of chainable continua produced by set-valued functions that are not mappings. The paper includes theorems on constructing subcontinua of inverse limits as well as theorems on expressing inverse limits with set-valued functions as inverse limits with mappings.
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