We defined gΔ* and gsΔ*-closed in terms of ideal spaces in the paper, and some of their properties and characterizations are discussed. Further, we study its interrelationships between some existing generalizations and are investigated these closed sets. The paper’s goal is to deepen the investigation of a few types of closed sets in ideal spaces which satisfies the Kuratowski closure operator. These sets exactly lies between δ* and Ig-closed sets.