Baire spaces and infinite games.

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  • Additional Information
    • Subject Terms:
      BAIRE spaces; INFINITE games (Game theory); BANACH spaces; TOPOLOGY; CARDINAL numbers
    • Abstract:
      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. [ABSTRACT FROM AUTHOR]
    • Abstract:
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