Technology Category
Multiagent Systems: Mechanism DesignGame Theory and Economic Paradigms: Cooperative Game TheoryKnowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
On Effective Banach-Mazur Games and an application to the Poincar'e Recurrence Theorem for Category
🤖 AI Summary
研究如何将Banach-Mazur游戏有效化，以表征有效第一范畴集，并应用于证明动态系统中的有效Poincaré回归定理。
Technology Category
Application Category
📝 Abstract
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 Poincar'e Recurrence. The Poincar'e Recurrence Theorem for category states that for a homeomorphism without open wandering sets, the set of non recurrent points forms a first category (meager) set. As an application of the effectivization of the Banach-Mazur game, we show that such a result holds true in effective settings as well.
Problem
Research questions and friction points this paper is trying to address.
Effectivizing Banach-Mazur game for first category sets
Proving effective Banach Category Theorem via games
Establishing effective Poincaré Recurrence for dynamical systems
Innovation
Methods, ideas, or system contributions that make the work stand out.
Effectivized Banach-Mazur game for category sets
Game-theoretic proof for effective Banach theorem
Effective Poincaré Recurrence via category game
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