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Tytuł artykułu

Stationary and convergent strategies in Choquet games

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If Nonempty has a winning strategy against Empty in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows Nonempty to consider the entire finite history of previous moves before making each new move; a stationary strategy only permits Nonempty to consider the previous move by Empty. We show that Nonempty has a stationary winning strategy for every second-countable T₁ Choquet space. More generally, Nonempty has a stationary winning strategy for any T₁ Choquet space with an open-finite basis.
We also study convergent strategies for the Choquet game, proving the following results. A T₁ space X is the open continuous image of a complete metric space if and only if Nonempty has a convergent winning strategy in the Choquet game on X. A T₁ space X is the open continuous compact image of a metric space if and only if X is metacompact and Nonempty has a stationary convergent strategy in the Choquet game on X. A T₁ space X is the open continuous compact image of a complete metric space if and only if X is metacompact and Nonempty has a stationary convergent winning strategy in the Choquet game on X.
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  • Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, U.S.A.
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  • Department of Mathematics, Marshall University, 1 John Marshall Drive, Huntington, WV 25755, U.S.A.
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bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-1-5
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