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The Baire product theorem for Choquet spaces

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

Palomar Registrypalomar/PALOMAR-2026-10-20-000009Oct 20, 2026math.GNscore 0

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.

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