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Banach–Mazur determinacy for Baire-property targets

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

Palomar Registrypalomar/PALOMAR-2026-10-21-000013Oct 21, 2026math.GNscore 0

For any complete metric space and any target set with the property of Baire, the Banach–Mazur category game is determined: the first player has a winning full-history strategy exactly when the target is nonmeagre, and the second exactly when it is meagre. A win for the first player means one target point lies in every move. The proof constructs meagre-target avoidance without metric assumptions and shrinking closed-trap target forcing in complete metric spaces; it proves actual joint-play existence and excludes simultaneous winners. Empty spaces and equal nested moves are explicit. This is…

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