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- W2320857024 abstract "For a topological space $X$ and a point $x in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $ninomega$, the first player chooses a set $A_n$ that clusters at $x$, and then the second player picks a point $a_nin A_n$; the second player is the winner if and only if $xinoverline{{a_n:ninomega}}$. In this work, we study variations of this game in which the second player is allowed to choose finitely many points per inning rather than one, but in which the number of points they are allowed to choose in each inning has been fixed in advance. Surprisingly, if the number of points allowed per inning is the same throughout the play, then all of the games obtained in this fashion are distinct. We also show that a new game is obtained if the number of points the second player is allowed to pick increases at each inning." @default.
- W2320857024 created "2016-06-24" @default.
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- W2320857024 date "2016-03-31" @default.
- W2320857024 modified "2023-09-27" @default.
- W2320857024 title "Selective game versions of countable tightness with bounded finite selections" @default.
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- W2320857024 hasPublicationYear "2016" @default.
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