Normality of the Vietoris power V(ω^ω)
Determine whether the Vietoris power space V(ω^ω) is normal; that is, whether every pair of disjoint closed subsets of V(ω^ω) can be separated by disjoint open neighborhoods.
References
We use ? to indicate that we have not been able to verify whether the indicated space satisfies the indicated property, which we formalize as Question \ref{question:VBaire}. Is \mathsf V(\omega\omega) normal?
                — An Adaptation of the Vietoris Topology for Ordered Compact Sets
                
                (2507.17936 - Caruvana et al., 23 Jul 2025) in Question 4.? (labelled Question \ref{question:VBaire}), Subsection “The Vietoris Power on Subsets of Naturals”