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On non-separable components of hyperspaces with the Hausdorff metric |
| Author |
R. Cauty
cauty@math.jussieu.fr
Universite Paris 6, Institut de mathematiques de Jussieu
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| Abstract |
Let $(X,d)$ be a connected non compact metric space. Suppose the metric
$d$ convex and such that every closed bounded subset of $X$ is compact. Let $\mathcal F(X)$ be
the space of nonvoid closed subsets of $X$ with the Hausdorff distance associated to $d$.
We prove that every component of $\mathcal F(X)$ which contains an unbounded closed subset is
homeomorphic to the Hilbert space $\ell^2(2^{\aleph_0})$. |
| Keywords |
metric space; Hausdorff distance |
| DOI |
doi:10.30970/ms.35.1.91-105
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| Reference |
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– P. 193–217.
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P. 89–93.
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| Pages |
91-105 |
| Volume |
35 |
| Issue |
1 |
| Year |
2011 |
Journal |
Matematychni Studii |
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