Title
Stationary and convergent strategies in Choquet games
Document Type
Article
Publication Date
2010
Abstract
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.
Recommended Citation
F. G. Dorais and C. Mummert, Stationary and convergent strategies in Choquet games, Fundamenta Mathematicae 209 (2010) 59-79.
Comments
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