Abstract In this paper, we show that the class of aposyndetic continua can be partitioned, using the notion of dimension, into countably many subclasses, each of which, except for one, has no common model and contains a continuum-sized subfamily of mutually incomparable continua. Whether a common model or a continuum-sized subfamily of mutually incomparable continua exists for this exceptional subclass remains open.
Eiichi Matsuhashi (Fri,) studied this question.