{"id":"palomar/PALOMAR-2026-10-20-000009","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/51def6feb5e4469cce2396dfa4c9fa4f3b933d82/topology/choquet-baire-product","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-20-000009-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54E52","msc:54B10","msc:91A44","general-topology","baire-spaces","choquet-spaces","banach-mazur-game"],"score":0,"title":"The Baire product theorem for Choquet spaces","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":"An arbitrary Baire topological space times a space with a winning full-history second-player Banach–Mazur strategy is Baire. A disjoint dense rectangle tree yields, for each prescribed nonempty open fiber region, a dense Gδ set of parameters with a common-point fiber witness for every countable dense-open product family. An explicit shrinking-ball strategy establishes alpha-favorability of complete metric spaces. Empty factors and legal-play existence are treated explicitly. This is classical mathematics, not a novelty or determinacy claim.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-20","reactions":{},"formalized":true,"formalizes":[{"title":"More on products of Baire spaces, arXiv:1702.06197v3","identifier":"https://arxiv.org/pdf/1702.06197v3","relationship":"formalizes"}]}