On the strategies for NONEMPTY in topological games

The research article “On the strategies for NONEMPTY in topological games”, co-authored by METU member Prof. Süleyman Önal, has been published in Topology and its Applications.

We prove that if NONEMPTY has a Markov strategy in the Choquet game on a space X, then the player has a 2-tactic in that game. We also prove that if NONEMPTY has a k-Markov strategy in the Choquet game on a space X which has a Noetherian base with countable rank, then the player has a k-tactic in that game. We show that if NONEMPTY has a winning strategy in the Choquet game on a space X which has one of the some special bases including σ-locally countable bases, then the player has a 2-tactic in that game. We also show that if NONEMPTY has a winning strategy in the Choquet game on a space X which has some special Noetherian bases, then NONEMPTY has a stationary strategy, 1-tactic, in that game. We investigate some similar results for the Banach-Mazur game.

Önal, S., & Soyarslan, S. (2020). On the strategies for NONEMPTY in topological games. Topology and its Applications, 278 doi:10.1016/j.topol.2020.107236

Article access: https://www.sciencedirect.com/science/article/pii/S0166864120301796

Tags/Keywords:

Banach-Mazur game, Choquet game, Markov strategy, Noetherian base, Stationary strategies, Tactic, Topological games, Winning strategies

Other authors:
Soyarslan, S.

Acknowledgment:
The authors would like to thank Dr. Çetin VURAL for his contribution to this work.