$k$-Markov and $k$-Tactic for NONEMPTY in the Choquet Game
Keywords:
Choquet game, Markov strategy, stationary strategy, tactic, topological games, topological groupsAbstract
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 $\mathrm{s} / \mathrm{he}$ has a winning $k$-tactic in this game.
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