In this paper, we will study some of the properties of the operator Ԑ(Ⱨ) with respect to ∾- a topological space defined by a cluster system, some of which are unconditionally true and others are conditionally true. We will also discuss some important theorems about operators ∾-interior and ∾-closure, and use these concepts to define operators ∾ℇ-volterra and weakly ∾ℇ-Volterra. We will also review the relationship between these two concepts. In addition, we will present some basic theorems about these two concepts.