Topolojik Oyunlarda Örtüsel Özellikler

Abstract

This thesis consists of five chapters. The first chapter is devoted to game theory and the historical development of topological games, which is the subject of the thesis. In the second part, some definitions and theorems that will be used in the thesis are given. In the third chapter, Menger and Rothberger covering properties are defined and some examples providing these properties are given. In the fourth chapter, topological games are examined in detail. Some examples of games such as point-open game, Rothberger game, Menger game are given and these games are examined with winning strategies. In addition, the concepts of equivalent and dual games are also defined. In the fifth chapter, which is the last chapter, Banach-Mazur games, which form the basis of game theory and are associated with Baire Category theorem, are included. In addition, D-spaces and their relations with covering properties are also examined.