A Banach-Mazur game $MB(X,Y, \mathcal W)$ is a topological game played as follows:
Let $X$ be a topological space, $Y$ a fixed subset of $X$, and $\mathcal W$ a family of subsets of $X$ such that
Players 1 and 2 take turns picking elements of $\mathcal W$ in a sequence $W_1\supset W_2\supset\cdots$. Player 1 wins if and only if \(Y\cap \left(\bigcap_{n<\omega} W_n\right)\) is nonempty. If Player 1 loses, Player 2 wins.
Wikidata ID: Q3459695