Hereditarily unicoherent continua and their absolute retracts
The authors consider absolute retracts for several classes of spaces. Of special interest are the classes of all hereditarily unicoherent continua, tree-like continua, \(\lambda\)-dendroids, and dendroids. A long term goal of their study is to find characterizations of absolute retracts for these classes of spaces. They prove among other things that the inverse limit of a sequence of trees with confluent bonding maps is an absolute retract for the class of all hereditarily unicoherent continua. As corollaries they obtain that Knaster type continua and each fan with the property of Kelly are absolute retracts. They also prove that each tree-like continuum is a subspace of a tree-like continuum that is the inverse limit of a sequence of trees with open (thus confluent) bonding maps. From this result they conclude that there exist non-arcwise connected \(\lambda\)-dendroids that are absolute retracts for the class of all hereditarily unicoherent continua. The paper concludes with several interesting open problems.
scientific article; zbMATH DE number 2103617
scientific article