Topological structures of hyperspaces of finite sets in non-separable metrizable spaces

Katsuhisa Koshino

Published 2015-08-31Version 1

Let ${\rm Fin}(X)$ be the hyperspace consisting of non-empty finite subsets of a space $X$ endowed with the Vietoris topology. In this paper, we characterize a metrizable space $X$ whose hyperspace ${\rm Fin}(X)$ is homeomorphic to the linear subspace spanned by the canonical orthonormal basis of a non-separable Hilbert space of density $< \mathfrak{d}$, where $\mathfrak{d}$ is the dominating number.