Talk:Banach–Mazur game

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Feel free to edit/correct mistakes, etc. I'm not an expert on this, so I'm sure others could add more insight. Revolver

I'm not sure I got the last part right, about Baire spaces. I'm pretty tired. Check that out. Revolver

I removed this:

The relationship of the Banach-Mazur game to Baire spaces follows immediately from the above result:

Let X be a topological space. Then there exists a subset C of X such that Player II does not have a winning strategy if and only if X is a Baire space.

This statement seems to use the conjecture that a space X is Baire iff X has a non-meagre subset, i.e. iff X is of second category. But that conjecture is false, as was pointed out by an anonymous contributor on Baire space. AxelBoldt 18:39, 16 Dec 2003 (UTC)

[edit] Which player is trying to get into the set?

The article has II winning if the final point winds up in the set determining the Banach-Mazur game. Moschovakis has it the other way; I is trying to get into the set. Obviously it doesn't really matter mathematically, but I want to put a link to this article from Determinacy, and I think it's confusing if usual games are defined with I trying to get into the set, and Banach-Mazur games are defined the opposite way.

Would anyone object if I switched it, and changed other things to match? --Trovatore 05:21, 3 September 2005 (UTC)