Baire spaces and infinite games
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It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.
KeywordsBaire space Infinite game Measurable cardinal
Mathematics Subject Classification03E55 03E60 03E65 54B10 54E52 91A44 91A46
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