In this paper we introduce the notion of $\hat\omega$-closed sets in
topological spaces and obtain some of the basic properties of this class of sets.
Further more their relationships with other generalized closed sets are investigated.
It turns out that this class lies between the class of $a$-closed sets
and the class of $g\alpha$-closed sets. And some $\hat{\omega}$-closure formulas in subspaces are investigated
in the end of the present paper.