A minicourse on topological games

Abstract

The purpose of these notes is to introduce the basics of topological games and some of the techniques used in the field to the uninitiated reader. We deal mostly with games involving covering properties and variations of countable tightness, with some emphasis on selective topological games — such as the Rothberger game G1(O,O) and the Menger game Gfin(O,O). We also illustrate how topological games can be used in contexts that are not game-theoretical in essence, such as preservation of topological properties in products and the D-space problem.