2 problems

Let $X$ be a space, and let $CL(X)$ denote the hyperspace of nonempty closed subsets of $X$ with Vietoris topology $fmathbb{V}$. Conjecture 2. $(CL(X), \mathbb{V})$ is quasi-metriz…

Let $X$ be a space. Write $CL(X)$ for the hyperspace of nonempty closed subsets of $X$, equipped with the Vietoris topology $fmathbb{V}$. A topological sum is denoted by…