Stationary and convergent strategies in Choquet games

• Autorzy: François G. Dorais , Carl Mummert
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 06B35: Continuous lattices and posets, applications
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 209
• Numer: 1
• Strony: 59-79

Daty

wydano

2010

Twórcy

autor

François G. Dorais

• Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, U.S.A.

autor

Carl Mummert

• Department of Mathematics, Marshall University, 1 John Marshall Drive, Huntington, WV 25755, U.S.A.

Identyfikatory

DOI

10.4064/fm209-1-5