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On Effective Banach-Mazur Games and an application to the Poincar\'e Recurrence Theorem for Category
Prajval Koul, Satyadev Nandakumar
https://arxiv.org/abs/2506.11118

On Effective Banach-Mazur Games and an application to the Poincaré Recurrence Theorem for Category
The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we give a proof for the effective Banach Category Theorem. Further, we provide a game-theoretic proof of an effective theorem in dynamical systems, namely the category version of Poincaré Recurrence. The Poincaré Recurrence Theorem for category states that for a hom…