k-Markov and k-Tactic for NONEMPTY in the Choquet Game - Önal, Süleyman; Soyarslan, Servet (Topology Proceedings, 2021)
There is an open question in the Choquet game about existence of NONEMPTY’s winning 1-tactic whenever s/he has a Markov winning strategy in the Choquet game (Galvin). In a more general version, we can ask the question: If NONEMPTY has a k Markov winning strategy in the Choquet game, does NONEMPTY have a winning k-tactic in that game? In some special topological spaces, we give some affirmative answers to this question. For example, we show that if NONEMPTY has a k-Markov winning strategy in the Choquet game on a topological group or on a space in which all points are P -points, then s / he has a winning k-tactic in this game.