Star and strongly star selection principles

In this thesis, more general forms of compactness, which is an important topological property, are studied. The studies on the theory of star-compactness and star-selection have been investigated so far, and the main parts of the subject have been compiled with the proofs. This thesis consists of five chapters. In the first chapter, the theory of selection principles is briefly mentioned. In the first part of the second chapter, preliminary informations and basic concepts are given, and in the second part of the second chapter, the covering properties and -compactness and classical selection principles are included. In the first part of the third chapter, the concepts of new covering types and star selection principles are mentioned. The first part of the third chapter, which forms the main part of the thesis, is divided into two subsections. In the first subsection, star-compactness, in the second subsection, star-Menger-type selection principles and strongly-star-Menger-type selection principles are examined. In the fourth section, suggestions are made by evaluating the results obtained. In the last section, references are included. Keywords: Selection Principles Theory, Star Selection Principles, Star Compactness, Open Cover