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

Abstract

Let $\mathrm{Fin}(X)$ 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 $\mathrm{Fin}(X)$ is homeomorphic to the linear subspace spanned by the canonical orthonormal basis of a non-separable Hilbert space.

arXiv commentLemma 4.1 and Proposition 4.2 has been revised because there is a gap in the proof. arXiv admin note: substantial text overlap with arXiv:1503.08575