On generalizedω-closed sets

Abstract

The class ofω-closed subsets of a space(X,τ)was defined to introduceω-closed functions. The aim of this paper is to introduce and study the class ofgω-closed sets. This class of sets is finer thang-closed sets andω-closed sets. We study the fundamental properties of this class of sets. In the space(X,τω), the concepts closed set,g-closed set, andgω-closed set coincide. Further, we introduce and studygω-continuous andgω-irresolute functions.