The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications
The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications
Given an arbitrary spectral space $X$, we consider the set $\mathcal{X} (X)$ of all nonempty subsets of $X$ that are closed with respect to the inverse topology. We introduce a Zariski-like topology on $\mathcal{X} (X)$ and, after observing that it coincides the upper Vietoris topology, we prove that $\mathcal{X} (X)$ …