Let  be topological space. A subset A of X is called a generalized semi-closed set (pure-gsc) set if  whenever  and U is open in X [2]. We note that the intersection of two pure-gsc set need not be a pure-gsc set. So that  is a pure-gsc set} is not a topology in X. However, if we define a gsc set as an arbitrary intersection of pure-gsc sets, it can be shown that  is a gsc set} is a topology in X. Moreover, if  is the intersection of all pure gsc-sets containing A, then the function  given by  is a Kuratowski closure operation.

Furthermore, we used the concept gsc set to define some functions (e.g., gs^*-irresolute, pre-gs-closed, gs^*-closed, gs^*-continuous, gs^*-homeomorphism) that are parallel to the ones that are presented in [6]. We gave some of their properties.

pure-gsc set, gsc set, gs^*-irresolute, pre-gs-closed, gs^*-continuous function, gs^*-homeomorphism.