Hyperspaces of Peano continua are Hubert cubes
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D. Curtis, R. Schori (1978)
Fundamenta Mathematicae
Helma Gladdines, Jan van Mill (1993)
Fundamenta Mathematicae
If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space is homeomorphic to , where B denotes the pseudo-boundary of the Hilbert cube Q.
D. Curtis, R. Schori (1978)
Fundamenta Mathematicae
Louis J. Nachman (1968)
Mathematica Scandinavica
Michael Levin, Yaki Sternfeld (1996)
Fundamenta Mathematicae
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 with . This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.
Paweł Krupski (2002)
Colloquium Mathematicae
It is shown that the following hyperspaces, endowed with the Hausdorff metric, are true absolute -sets: (1) ℳ ²₁(X) of Sierpiński universal curves in a locally compact metric space X, provided ℳ ²₁(X) ≠ ∅ ; (2) ℳ ³₁(X) of Menger universal curves in a locally compact metric space X, provided ℳ ³₁(X) ≠ ∅ ; (3) 2-cells in the plane.
Paweł Krupski (1999)
Acta Universitatis Carolinae. Mathematica et Physica
Laurence Boxer (1983)
Fundamenta Mathematicae
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