The space of subcontinua of a 2-dimensional continuum is infinite dimensional
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- by Michael Levin and Yaki Sternfeld PDF
- Proc. Amer. Math. Soc. 125 (1997), 2771-2775 Request permission
Abstract:
Let $X$ be a metric continuum and let $\mathcal {C}(X)$ denote the space of subcontinua of $X$ with the Hausdorff metric. We settle a longstanding problem showing that if $\dim X = 2$ then $\dim \mathcal {C}(X)= \infty$. The special structure and properties of hereditarily indecomposable continua are applied in the proof.References
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Additional Information
- Michael Levin
- Affiliation: Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel
- Email: levin@mathcs2.haifa.ac.il
- Yaki Sternfeld
- Affiliation: Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel
- Email: yaki@mathcs2.haifa.ac.il
- Received by editor(s): February 4, 1995
- Received by editor(s) in revised form: March 31, 1996
- Communicated by: James West
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2771-2775
- MSC (1991): Primary 54B20, 54F15, 54F45
- DOI: https://doi.org/10.1090/S0002-9939-97-04172-5
- MathSciNet review: 1425131