Hereditarily weakly confluent maps and a characterization of class \(HW\) (Q1962102)

A continuum \(X\) is said to be in class HW provided that for every continuum \(Y\) any map \(f: Y\to X\) from \(Y\) onto \(X\) is hereditarily weakly confluent. In 1979 Grispolakis and Tymchatyn proved that atriodic, tree-like continua are in class HW and in 1984 Davis proved that atriodic acyclic curves are in class HW. In this paper, the authors prove a rather artificial theorem characterizing class HW. They also prove that the image of any hereditarily unicoherent continuum under a hereditarily weakly confluent map is also hereditarily unicoherent.