Abstract
We prove basic results about the set function \(\mathcal {T}\) 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 \(\mathcal {T}\). The notion of aposyndesis is the main motivation of Jones to define this function. We study the idempotency of T on products, cones and suspensions. We present some properties of a continuum assuming the continuity of the set function T and examples of classes of continua for which T is continuous. We give three decomposition theorems using \(\mathcal {T}\). We also present some applications.
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