A new class between theta open sets and theta omega open sets

We define $$ -closure operator as a new topological operator which lies between the θ-closure and the $$ -closure. Some relationships between this new operator and each of θ-closure, $$ -closure, and usual closure are obtained. Via $$ -closure operator, we introduce $$ -open sets as a new topology. Some mapping theorems related to the new topology are given. $$ topological spaces are characterized in terms of $$ -closure operator. Also, we use $$ -open sets to define $$ -regularity as a new separation axiom which lies strictly between ω-regularity and regularity. For a given topological space $$ , we show that $$ -regularity is equivalent to the condition $$ . Finally, $$ -continuity, $$ -θ-continuity, weak $$ -continuity, and faint $$ -continuity are introduced and studied.