Generalized closed sets and some separation axioms on weak structure

Abstract

In this paper, we introduce and characterize the concepts of generalized closed (gw-closed, for short) sets in weak structures which introduced by Császár [3] and we give some properties of these concepts. The concept of gw-closed sets (in the sense of Al Omari and Noiri [1]) is a special case of gw-closed sets presented here. Finally, the concepts of T 1 2 -, T1-, normal, almost normal and weakly normal spaces are investigated by using the concepts of gw-closed, sgw-closed and mgw-closed sets in weak structures.