Açık Örtü Sınıflarına Dayalı Özellikler Üzerine Bir Çalışma

Abstract

he aim of this thesis is to make a compilation on the theory named as infinite combinatorialtopology or the selection principles in mathematics and to investigate the relations betweenthe sets of reals and Menger Conjecture.This thesis consists of five chapters. In the first chapter, the studies about selection principlesare briefly mentioned and the informations about the topic of the thesis are given. In the se-cond 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, theConjectures 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 relationsbetween 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 Lu-sin and scale sets can be constructed and those ones which are counter examples to MengerConjecture are introduced