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 $\ell_{2}(\tau) \times \ell_{2}^{f}$.
Citation
Masato Yaguchi. "Hyperspaces of finite subsets of non-separable Hilbert spaces." Tsukuba J. Math. 30 (1) 181 - 193, June 2006. https://doi.org/10.21099/tkbjm/1496165036
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