The Vietoris hyperspace of finite sets of Erd\H{o}s space

Abstract

Recently, David S. Lipham has shown that if $X$ is an Erd\H{o}s space factor then the Vietoris hyperspace $\mathcal{F}(X)$ of finite subsets of $X$ is an Erd\H{o}s space factor. In this short note we prove that if $\mathfrak{E}$ denotes Erd\H{o}s space then $\mathcal{F}(\mathfrak{E})$ is in fact homeomorphic to $\mathfrak{E}$.