On the image of Jones’ set function $\mathcal {T}$
Volume 153 / 2018
Colloquium Mathematicum 153 (2018), 1-19
MSC: Primary 54B20.
DOI: 10.4064/cm7037-4-2017
Published online: 12 March 2018
Abstract
We study possible images of Jones’ set function $\mathcal {T}$. In particular, we are interested in when either $\mathcal {T}(\mathcal {F}_1(X))$ or $\mathcal {T}(2^X)$ is finite or countable. We introduce the notion of $\omega $-indecomposable continuum as a generalization of the well known concept of $n$-indecomposable continuum. We also present results about connectedness and compactness of $\mathcal {T}(2^X)$. Finally, we give a generalization, to continua with the property of Kelley, of a couple of results known for homogeneous continua.
