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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 F(X) be
the space of nonvoid closed subsets of X with the Hausdorff distance associated to d.
We prove that every component of F(X) which contains an unbounded closed subset is
homeomorphic to the Hilbert space ℓ2(2ℵ0). |
| Keywords |
metric space; Hausdorff distance |
| Reference |
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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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