A survey on topological games and their applications in analysis.

*(English)*Zbl 1114.91024The authors discuss several types of infinite positional games and present some of their applications in topology. More precisely they recall main properties of the Choquet game, the Banach-Mazur game and some modifications of the Choquet game. Then they characterize links between the Choquet game and the Baireness of topological spaces and between the Banach-Mazur game (or more precisely its extension given by Oxtoby) and topological closed graph theorems. The first modification of the Choquet game is called a fragmenting game and is used to characterize such topological properties as fragmentability and membership in the class of weakly Stegall spaces. Some other modifications are used to find the Namioka property and to distinguish between different topological properties. Yet another game discussed in the paper is the Cantor game and it is used to distinguish membership in the class of weakly Stegall spaces and weakly Asplund spaces.

Reviewer: A. Šwierniak (Gliwice)

##### MSC:

91A44 | Games involving topology, set theory, or logic |

54E52 | Baire category, Baire spaces |

46B20 | Geometry and structure of normed linear spaces |

91A80 | Applications of game theory |

91A24 | Positional games (pursuit and evasion, etc.) |

54A05 | Topological spaces and generalizations (closure spaces, etc.) |

54C65 | Selections in general topology |