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