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

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