Hereditarily weakly confluent maps and a characterization of Class HW

First it is proved that the image of any hereditarily unicoherent continuum under a hereditarily weakly confluent map is also hereditarily unicoherent. This answers a question raised in 1979 by T. Maćkowiak. Second, a characterization is established for Class HW, i.e., for the class of all continua Y such that each mapping from a continuum onto Y is hereditarily weakly confluent. That characterization is used to prove J.F. Davisʹ theorem that atriodic, acyclic curves are in Class HW.