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Stationary and convergent strategies in Choquet games

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Dorais F., Mummert C.

Fundamenta Mathematicae

2010

tom 209

nr 1

59-79

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Dorais F.

1 Mummert C.

1 2010

Wyniki wyszukiwania

Stationary and convergent strategies in Choquet games