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