New G-Closed Sets with Related to an Ideal

Ideal is a family which has two properties as known heredity and finite additive. Besides it is a partially ordered collection of sets. This using this concept with a topology was obtained a new topology finer than old. Elements of topology are open sets and their complements are closed sets. It is known that generalized closed set is weaker than closed. Then, several authors studied on this subject both topological spaces and ideal topological spaces. In this paper, we recall some concepts and their basic properties. Then, we introduce new g-closed set called \(*Ig\) -closed set by using ideal and obtained some properties of it. We have obtain a diagram showing the relationships between them and other types of g-closed sets in the literature. Besides, we define a concept of \(*Ig\) -open set and investigate it. We give that a family of consisting of this sets in any I-space forms a minimal structure. Finally, we mention when \(*Ig\) -closed is conserved.