ABSTRACT

The brass ring of selection theory-specifically with regard to continua-is to determine the necessary and sufficient conditions which specify the class of continua which are selectible. It is well known that if a continuum is selectible then it is a dendroid. We also have numerous examples, though, of dendroids which do not admit a selection. Every dendrite is of course selectible, though we have a wide variety of selectible continua which are not dendrites. Somewhere nested between the dendroids and the dendrites in the obvious Venn diagram lies the brass ring.