Some bitopological forms and properties of selection principles

Covers are used to define various topological properties related to compactness. It is important to be able to collect and classify a topological space under certain classes using its covers. The Theory known as Selection Principles in topology has an important place in this field. It allows characterizing a wide range of topological notions, obtaining a different cover of a given topological space by using its different open covers, and collecting the related topological space into desired classes. The selection principles theory, which brought topology with other fields of mathematics, such as game theory, function spaces, etc., is still actively studied. The Menger property, which lies between compactness and Lindelöf property, is one of the most essential covering property of selection principles. In this thesis, some weaker and general forms of the Menger, Alster, and Lindelöf covering properties are defined in bitopological spaces. Firstly, some weaker forms of the Menger and Lindelöf properties are defined and examined by using closure, interior, and star operators. Afterwards, the bitopological nearly Alster property, which is a bitopological form of the Alster property, is introduced and some topological properties of bitopological spaces that have this property are scrutinized. Some of defined properties are characterized in terms of selection principles. The bitopological almost Rothberger and bitopological weakly Rothberger, which are the weaker forms of the Rothberger property existing in the literature, are studied in detail. With these new forms, the thesis study is regarded as a continuation of the field of selection principles and selective covering properties via bitopological spaces.