An effectivized Banach-Mazur game is claimed to characterize effective first category sets and to prove an effective category version of Poincaré recurrence.
Computable metrization.Math
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On Effective Banach-Mazur Games and an application to the Poincar\'e Recurrence Theorem for Category
An effectivized Banach-Mazur game is claimed to characterize effective first category sets and to prove an effective category version of Poincaré recurrence.