Weak and relative forms of some selection properties

The aim of this thesis is to introduce the weak forms of some classical selection properties in bitopological spaces, investigate the relationships between them and characterize these properties with topological games. This thesis consists of five chapters. In the first chapter, information about the topic of the thesis is given. In the second chapter, basic information about classical selection principles, topological games and bitopological spaces to be used in the thesis is given. In the third chapter, weak Menger properties are defined in the bitopological spaces, the relationships of these properties with one another and the classical selection principles are studied, and also some topological properties of them are discussed. Finally, in this chapter, Hurewicz property, which is a classical selection principle, is defined. The fourth chapter is devoted to the weak forms of Alster property in bitopological spaces. In this context, almost Alster and weakly Alster properties are introduced and these properties are characterized with selection principles. In addition, it is shown that the almost Alster bitopological spaces are productively Lindelöf. The final chapter is about the applications of the weak selection principles to the game theory. In this chapter, the games parallel to the almost Menger and almost Alster properties in bitopological spaces are defined and relationships between games and these properties are examined.