The space of subcontinua of a 2-dimensional continuum is infinite dimensional

Michael Levin, Yaki Sternfeld

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Let X be a metric continuum and let C(X) denote the space of subcontinua of X with the Hausdorff metric. We settle a longstanding problem showing that if dim X = 2 then dimC(JV) = ∞. The special structure and properties of hereditarily indecomposable continua are applied in the proof.

Original languageEnglish
Pages (from-to)2771-2775
Number of pages5
JournalProceedings of the American Mathematical Society
Volume125
Issue number9
DOIs
StatePublished - 1 Jan 1997
Externally publishedYes

Keywords

  • 2-dimensional continua
  • Hereditarily indecomposable continua
  • Hyperspaces

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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