Stationary Strategies in Topological Games

Fred Galvin

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On a modified game of Sierpiński

Grzegorz Kubicki (1987)

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A survey on topological games and their applications in analysis.

Jiling Cao, Warren B. Moors (2006)

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In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.

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A. Zięba (1957)

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Rastislav Telgársky (1987)

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On a game of Sierpiński

Grzegorz Kubicki (1987)

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A dichotomy on Schreier sets

Robert Judd (1999)

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We show that the Schreier sets $S_{α} (α < ω_{1})$ have the following dichotomy property. For every hereditary collection ℱ of finite subsets of ℱ, either there exists infinite $M = {(m_{i})}_{i = 1}^{\infty} \subseteq ℕ$ such that $S_{α} (M) = m_{i} : i \in E : E \in S_{α} \subseteq ℱ$ , or there exist infinite $M = {(m_{i})}_{i = 1}^{\infty}, N \subseteq ℕ$ such that $ℱ [N] (M) = m_{i} : i \in F : F \in ℱ a n d F \subset N \subseteq S_{α}$ .

On game-theoretic methods in the theory of Souslin sets

Ashok Maitra (1971)

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Stationary and convergent strategies in Choquet games

François G. Dorais, Carl Mummert (2010)

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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...