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On the image of Jones’ set function $\mathcal {T}$

Volume 153 / 2018

Javier Camargo, Sergio Macías, Carlos Uzcátegui 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.

Authors

  • Javier CamargoEscuela de Matemáticas
    Facultad de Ciencias
    Universidad Industrial de Santander
    Ciudad Universitaria
    Carrera 27 Calle 9
    Bucaramanga, Santander, A.A. 678, Colombia
    e-mail
  • Sergio MacíasInstituto de Matemáticas
    Universidad Nacional Autónoma de México
    Circuito Exterior, Ciudad Universitaria
    México D.F., C.P. 04510, México
    e-mail
  • Carlos UzcáteguiEscuela de Matemáticas
    Facultad de Ciencias
    Universidad Industrial de Santander
    Ciudad Universitaria
    Carrera 27 Calle 9
    Bucaramanga, Santander, A.A. 678, Colombia
    e-mail

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