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Characterization of $\sigma $-porosity via an infinite game

Volume 216 / 2012

Martin Doležal Fundamenta Mathematicae 216 (2012), 109-118 MSC: 28A05. DOI: 10.4064/fm216-2-2

Abstract

Let $X$ be an arbitrary metric space and $P$ be a porosity-like relation on $X$. We describe an infinite game which gives a characterization of $\sigma $-$P$-porous sets in $X$. This characterization can be applied to ordinary porosity above all but also to many other variants of porosity.

Authors

  • Martin DoležalDepartment of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail

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