Baire Spaces and Infinite Games

Fred Galvin, Marion Scheepers

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
JournalMathematics Faculty Publications and Presentations
StatePublished - 1 Feb 2016

Keywords

  • 03E55
  • 03E60
  • 03E65
  • baire space
  • infinite game
  • measurable cardinal

EGS Disciplines

  • Mathematics

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