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Sneider's Gδ-diagonal metrization theorem

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-17-000003Oct 17, 2026math.GNscore 0

A compact Hausdorff space is metrizable if and only if its diagonal is a Gδ subset of its square with the product topology. The proof supplies a cofinal countable family of finite intersections of closed diagonal neighborhoods and an actual metric inducing exactly the given topology. The underlying type is arbitrary and may be empty. A general supporting theorem proves countable neighborhood character of every closed Gδ set in a compact normal space. This is classical mathematics; no novelty or priority is claimed.

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