hβ-local functions in ideal topological spaces

This thesis introduces and systematically investigates the concept of the hβ-local function, drawing upon the definition of h-open sets proposed by Fadhil Abbas. The thesis is divided into five chapters. Chapter One provides an introduction to the study, outlining key concepts that serve as the theoretical foundation for the research. Chapter Two presents the core notions of ideal topological spaces, which are utilized throughout the thesis. In Chapter Three, the author defines hβ-open sets and offers a comparative discussion with h-open and semi h-open sets, illustrated by pertinent examples. Chapter Four explores hβ-neighborhoods and hβ-open neighborhoods, offering an in-depth analysis of hβ-local functions with practical illustrations. The chapter also introduces the Cl* hβ operator*, supported by related theorems and examples. Finally, Chapter Five introduces g -hβ-closed sets and s*g-hβ-closed sets*, and