Abstract

We prove that if $X$ is a separable metric space with the Hurewicz covering property, then the Banach-Mazur game played on $X$ is determined. The implication is not true when ``Hurewicz covering property" is replaced with ``Menger covering property".

Keywords: Baire space; First category; Banach-Mazur game; Menger property; Hurewicz property.

MSC: 03E99, 54D20, 54E52

Pages:  195$-$202     

Volume  61 ,  Issue  3 ,  2009