## The Banach–Mazur game and σ-porosity

### Volume 150 / 1996

Fundamenta Mathematicae 150 (1996), 197-210
DOI: 10.4064/fm-150-3-197-210

#### Abstract

It is well known that the sets of the first category in a metric space can be described using the so-called Banach-Mazur game. We will show that if we change the rules of the Banach-Mazur game (by forcing the second player to choose large balls) then we can describe sets which can be covered by countably many closed uniformly porous sets. A characterization of σ-very porous sets and a sufficient condition for σ-porosity are also given in the terminology of games.