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

Michael Levin; Yaki Sternfeld

doi:10.1090/s0002-9939-97-04172-5

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

Michael Levin, Yaki Sternfeld

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	2771-2775
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	125
Issue number	9
DOIs	https://doi.org/10.1090/s0002-9939-97-04172-5
State	Published - 1 Jan 1997
Externally published	Yes

Keywords

2-dimensional continua
Hereditarily indecomposable continua
Hyperspaces

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9939-97-04172-5

Cite this

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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.",

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AB - 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.

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KW - Hereditarily indecomposable continua

KW - Hyperspaces

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

Abstract

Keywords

ASJC Scopus subject areas

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