On non-separable components of hyperspaces with the Hausdorff metric

R. Cauty

	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
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
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Pages	91-105
Volume	35
Issue	1
Year	2011
Journal	Matematychni Studii
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