An uncountable collection of Case-Chamberlin type continua with no model

An uncountable collection G of one-dimensional Continua is constructed, each of which is an inverse limit on figure-eights and is not tree-like. It is shown that each member of this collection is in Class(W) and has positive, surjective symmetric span. Furthermore, it is shown that if M is a compact metric continuum then there is a member of G which is not a continuous image of M. Also, conditions are given under which any mapping of a compact metric continuum onto a one-dimensional continuum X must be weakly confluent with respect to one of a given collection of subcontinua of X.