We define the θ ω-closure operator as a new topological operator. We show that θ ω-closure of a subset of a topological space is strictly between its usual closure and its θ-closure. Moreover, we give several sufficient conditions for the equivalence between θ ω-closure and usual closure operators, and between θ ω-closure and θ-closure operators. Also, we use the θ ω-closure operator to introduce θ ω-open sets as a new class of sets and we prove that this class of sets lies strictly between the class of open sets and the class of θ-open sets. We investigate θ ω-open sets, in particular, we obtain a product theorem and several mapping theorems. Moreover, we introduce ω-T 2 as a new separation axiom by utilizing ω-open sets, we prove that the class of ω-T 2 is strictly between the class of T 2 topological spaces and the class of T 1 topological spaces. We study relationship between ω-T 2 and ω-regularity. As main results of this paper, we give a characterization of ω-T 2 via θ ω-closure and we give characterizations of ω-regularity via θ ω-closure and via θ ω-open sets.