Geodesic
Hyperspaces of two-dimensional continua
Fundamenta Mathematicae, Tome 150 (1996) no. 1, pp. 17-24

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let X be a compact metric space and let C(X) denote the space of subcontinua of X with the Hausdorff metric. It is proved that every two-dimensional continuum X contains, for every n ≥ 1, a one-dimensional subcontinuum $T_n$ with $dim C (T_n) ≥ n$. This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.
DOI : 10.4064/fm-150-1-17-24
Keywords: hyperspaces, hereditarily indecomposable continua, one- and two-dimensional continua

Michael Levin 1 ; Yaki Sternfeld 1

1 
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Michael Levin; Yaki Sternfeld. Hyperspaces of two-dimensional continua. Fundamenta Mathematicae, Tome 150 (1996) no. 1, pp. 17-24. doi: 10.4064/fm-150-1-17-24

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