New definitions of open sets in ideal topological spaces

The first chapter of this thesis consists of the introduction, which provides a review of the literature on open and closed sets in topological and ideal topological spaces. The second chapter presents the definitions and properties of ideal topological spaces and some generalized sets, which will be utilized in subsequent chapters. The third chapter discusses the properties of γ- β-open and γ- β-closed sets formed using the γ operation, as well as γ- β-continuous functions. The fourth chapter, which is original, transfers the γ- β-open sets defined by the γ operation to ideal topological spaces. Keywords: Ideal topological Spaces, γ-β-I open sets, γ-β-I continuity