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Oxtoby's Banach–Mazur characterization of Baire spaces

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

Palomar Registrypalomar/PALOMAR-2026-10-20-000008Oct 20, 2026math.GNscore 0

An arbitrary topological space is Baire if and only if the first player has no winning full-history strategy in the nested nonempty-open Banach–Mazur game. The proof constructs a compatible play with one common point from disjoint dense response levels, and constructs a winning strategy from failure of Baireness. It separately verifies compatible-play existence, equality of the two players’ intersections and the empty-space boundary. No separation, countability or metric hypothesis is imposed. This is classical mathematics, not a novelty or determinacy claim.

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