Topological games and products, II

Yukinobu Yajima

Displaying similar documents to “Topological games and products, II”

Topological games and products, III

Yukinobu Yajima (1983)

Fundamenta Mathematicae

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On some topological games

Telgársky, R.

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A game and its relation to netweight and D-spaces

Gary Gruenhage, Paul Szeptycki (2011)

Commentationes Mathematicae Universitatis Carolinae

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We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.

On game-theoretic methods in the theory of Souslin sets

Ashok Maitra (1971)

Fundamenta Mathematicae

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Remarks on a game of Choquet

Rastislav Telgársky (1987)

Colloquium Mathematicae

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Some applications of game determinacy

G. Debs, J. Saint Raymond (1996)

Acta Universitatis Carolinae. Mathematica et Physica

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A dichotomy on Schreier sets

Robert Judd (1999)

Studia Mathematica

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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 $ℱ [N] (M) = m_{i} : i \in F : F \in ℱ a n d F \subset N \subseteq S_{α}$ .

A class of extensions of Restricted (s,t)-Wythoff’s game

Sanyang Liu, Haiyan Li (2017)

Open Mathematics

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Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the...