ON THE GENERALIZED SEMI-CLOSED SETS IN TOPOLOGICAL SPACES
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.