In mathematics, a Choquet game, introduced by Gustave Choquet (1969), is a topological game where two players take turns decreasing the size of a non-empty open subset of a topological space, and the first player wins if after an infinite number of moves the open sets have empty intersection. A nonempty topological space where the second player has a winning strategy is called a Choquet space.
A nonempty topological space where the first player has no winning strategy is the same as a Baire space, so in particular every Choquet space is a Baire space. However there are separable metric spaces where neither player has a winning strategy, so there are Baire spaces that are not Choquet spaces. Every nonempty complete metric space or nonempty locally compact Hausdorff space is a Choquet space.