Monotone maps of hereditarily indecomposable continua

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Abstract

We prove that every hereditarily indecomposable continuum is the image under an open, monotone map of a one-dimensional hereditarily indecomposable continuum. Thus there exists a one-dimensional hereditarily indecomposable continuum with infinite dimensional hyperspace.

Original languageEnglish
Pages (from-to)361-364
Number of pages4
JournalProceedings of the American Mathematical Society
Volume75
Issue number2
DOIs
StatePublished - Jul 1979

Keywords

  • Continuum
  • Hyperspace
  • Indecomposable
  • Monotone

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