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Cells and $n$-fold hyperspaces

Volume 145 / 2016

Javier Camargo, Daniel Herrera, Sergio Macías Colloquium Mathematicum 145 (2016), 157-166 MSC: Primary 54B20. DOI: 10.4064/cm6527-1-2016 Published online: 25 April 2016

Abstract

We prove that $X$ is a hereditarily indecomposable metric continuum if and only if the $n$-fold hyperspace ${\mathcal C}_n(X)$ does not contain $(n+1)$-cells, for any positive integer $n$. Also we characterize the class of continua whose $n$-fold hyperspaces and $n$-fold hyperspace suspensions are cells.

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
  • Daniel HerreraEscuela 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. Mexico
    and
    School of Mathematics
    University of Birmingham
    Birmingham, B15 2TT, UK
    e-mail
    e-mail

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