Jones’s Set Function 𝒯
We prove basic results about the set function 𝒯 defined by F. Burton Jones . We define this function on compacta and then we concentrate on continua. In particular, we present some of the well known properties (such as connectedness im kleinen, local connectedness, semi–local connectedness, etc.) using the set function 𝒯. The notion of aposyndesis was the main motivation of Jones to define this function. We present some properties of a continuum assuming the continuity of the set function 𝒯. We also give some applications.