English

Baire spaces and infinite games

Logic 2014-10-28 v2 General Topology

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 topology. The converse of this implication may be true also: 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.

Keywords

Cite

@article{arxiv.1401.6061,
  title  = {Baire spaces and infinite games},
  author = {Fred Galvin and Marion Scheepers},
  journal= {arXiv preprint arXiv:1401.6061},
  year   = {2014}
}

Comments

21 pages

R2 v1 2026-06-22T02:53:21.859Z