Some variations of the Banach-Mazur game
Leandro Fiorini Aurichi, Maddalena Bonanzinga, Gabriel Andre Asmat, Medina
TL;DR
This paper explores two new variations of the classical Banach-Mazur game, enhancing understanding of their connections to the Baire property and productively Baire spaces.
Contribution
It introduces and analyzes two novel variations of the Banach-Mazur game, deepening the theoretical link to Baire-related properties.
Findings
New game variations are more closely related to Baire properties.
The variations provide insights into productively Baire spaces.
Theoretical implications for topology and game theory.
Abstract
The classical Banach-Mazur game is directly related to the Baire property and the property of being a productively Baire space. In this paper, we discuss two variations of this classic game that are even more related to these properties.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Geometric and Algebraic Topology · Mathematical Dynamics and Fractals