{"id":"palomar/PALOMAR-2026-10-17-000003","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/497432e5e02244f242cdfc8c0a43316de3aa5bdc/topology/sneider-diagonal","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-17-000003-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54E35","msc:54D30","general-topology","metrization","lean-formalization","compact-spaces"],"score":0,"title":"Sneider's Gδ-diagonal metrization theorem","trust":"high","domain":"math.GN","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"math.GN","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-17","reactions":{},"formalized":true,"formalizes":[{"title":"Spaces having a small diagonal, arXiv:math/9910153v1","identifier":"https://arxiv.org/pdf/math/9910153v1","relationship":"formalizes"}]}