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A survey on topological games and their applications in analysis. (English) Zbl 1114.91024
The 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.

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
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