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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.

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Background

Beyond basic metrizability and compactness questions, the separation properties of V(ωω) remain unsettled. The authors list normality as one of the basic properties they have not been able to verify. Establishing normality (or its failure) would significantly position V(ωω) among classical non-metrizable separable Baire spaces (e.g., comparing to the Sorgenfrey line).

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”