ABSTRACT
This chapter proves basic results about the set function defined by F. Burton Jones. It defines this function on compacta and then concentrates on continua. In particular, the chapter presents some of the well known properties (such as connectedness im kleinen, local connectedness, semi–local connectedness, etc.) using the set function. The notion of aposyndesis was the main motivation of Jones to define this function. The chapter presents some properties of a continuum assuming the continuity of the set function, and also gives some applications.
