Soft θω-Open Sets and Soft θω-Continuity

The soft theta(omega)-closure operator is defined as a new soft operator that lies strictly between the usual soft closure and the soft theta-closure. Sufficient conditions are provided for equivalence between the soft theta(omega)-closure and usual soft closure operators, and between the soft theta(omega)-closure and soft theta-closure operators. Via the soft theta(omega)-closure operator, the soft theta(omega)-open sets are defined as a new class of soft sets that lies strictly between the class of soft open sets and the class of soft theta-open sets. It is proven that the class of soft theta(omega)-open sets form a new soft topology. The soft w-regularity is characterized via both the soft theta(omega)-closure operator and soft theta(omega)-open sets. The soft product theorem and several soft mapping theorems are introduced. The correspondence between the soft topology of the soft theta(omega)-open sets of soft topological space and their generated topological spaces, and vice versa, are studied. In addition to these, soft theta(omega)-continuity as a strong form of soft theta-continuity is introduced and investigated.