A study on properties based upon the classes of open covers

The aim of this thesis is to make a compilation on the theory named as infinite combinatorial topology or the selection principles in mathematics and to investigate the relations between the sets of reals and Menger Conjecture. This thesis consists of five chapters. In the first chapter, the studies about selection principles are briefly mentioned and the informations about the topic of the thesis are given. In the second chapter, the general definitions, concepts and results will be used in the thesis are given. In the third chapter, the classes of covers and classical selection principles are presented, the Conjectures of Menger and Hurewicz are given and the relations between them investigated. In the fourth chapter, the sets of reals and relations between them are mentioned, the relations between the cardinals of the sets of reals and classical selection principles are scrutinized. Finally, in the fifth chapter, it is mentioned under what conditions some special sets like Lusin and scale sets can be constructed and those ones which are counter examples to Menger Conjecture are introduced.