Choquet game

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 an 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.

References

Choquet, Gustave (1969), Lectures on analysis. Vol. I: Integration and topological vector spaces, New York-Amsterdam: W. A. Benjamin, Inc., MR 0250011
Kechris, Alexander S. (1994). Classical Descriptive Set Theory. Springer-Verlag. ISBN 0-387-94374-9.

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