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The Space of subcontinua of a 2-dimensional continuum is infinite dimensional |
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| Authors: | Michael Levin Yaki Sternfeld |
| Affiliation: | Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel ; Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel |
| Abstract: | Let  be a metric continuum and let  denote the space of subcontinua of  with the Hausdorff metric. We settle a longstanding problem showing that if  then  . The special structure and properties of hereditarily indecomposable continua are applied in the proof. |
| Keywords: | Hyperspaces hereditarily indecomposable continua $2$-dimensional continua |
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