Tsukuba Journal of Mathematics

Hyperspaces of finite subsets of non-separable Hilbert spaces

Masato Yaguchi

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Abstract

Let $\ell_{2}(\tau)$ be the Hilbert space with weight $\tau$ and $\ell_{2}^{f}$ be the linear span of the canonical orthonormal basis of the separable Hilbert space $\ell_{2}$. In this paper, we prove that if a metric space $X$ ishomeomorphic to $\ell_{2}(\tau)$ or $\ell_{2](\tau) \times \ell_{2}^{f}$ then the hyperspace $Fin_{H}(X)$ of non-empty finite subsets of $X$ with the Hausdorff metric is homeomorphic to $\ell_{2}(\tau) \times \ell_{2}^{f}$.

Article information

Source
Tsukuba J. Math., Volume 30, Number 1 (2006), 181-193.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496165036

Digital Object Identifier
doi:10.21099/tkbjm/1496165036

Mathematical Reviews number (MathSciNet)
MR2248291

Zentralblatt MATH identifier
1117.46018

Citation

Yaguchi, Masato. Hyperspaces of finite subsets of non-separable Hilbert spaces. Tsukuba J. Math. 30 (2006), no. 1, 181--193. doi:10.21099/tkbjm/1496165036. https://projecteuclid.org/euclid.tkbjm/1496165036


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