This was the  rst in nite- positional game of perfect information to be studied.
This game, which is played with a  xed subset X of a topological space Y , is determined if X has the Baire property in Y . The second player has a winning strategy in this game if X is of the  rst category in Y , that is, if X is countable and Y is T1 and has no isolated points. This was the  rst in nite- positional game of perfect information to be studied. Identify this topological game in which two players alternate in choosing progressively nested members of a family of subsets of a topological space in an attempt to have their in nite intersection cover, or not cover, a  xed subset of that space, for   ten points.
This game, which is played with a  xed subset X of a topological space Y , is determined if X has the Baire property in Y .
Banach-Mazur game