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theorems/T000172.md

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After Player 1 chooses an open set $U_0$ and a point $x_0\in U_0$,
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Player 2 can choose a open neighborhood $V_0\subseteq U_0$ of $x_0$
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with $V_0$ homeomorphic to some $\mathbb R^n$ or $\mathbb R^n_+$.
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homeomorphic to some $\mathbb R^n$ or $\mathbb R^n_+$.
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The rest of the game is played on $V_0$ and Player 2 has a winning strategy
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since $\mathbb R^n$ and $\mathbb R^n_+$ are both {P206}
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[(Explore)](https://topology.pi-base.org/spaces?q=Completely+metrizable+%2B+%7EStrongly+Choquet).

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