Monotone images of W-sets and hereditarily weakly confluent images of continua

Abstract

A proper subcontinuum H of a continuum X is said to be a W-set provided for each continuous surjective function f from a continuum Y onto X, there exists a subcontinuum C of Y that maps entirely onto H. Hereditarily weakly confluent (HWC) mappings are those with the property that each restriction to a subcontinuum of the domain is weakly confluent. In this paper, we show that the monotone image of a W-set is a W-set and that there exists a continuum which is not in class W but which is the HWC image of a class W continuum.