On the image of Jones’ set function
Tom 153 / 2018
Colloquium Mathematicum 153 (2018), 1-19
MSC: Primary 54B20.
DOI: 10.4064/cm7037-4-2017
Opublikowany online: 12 March 2018
Streszczenie
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.
