Closure and Interior Operators of the Category of Positive Topologies

We define and study the notions of closure $\text{rsfs}\text{C}$ operators and interior $\mathbf{I}$ operators of the category $\mathbf{C}\mathbf{C}\mathbf{o}\mathbf{v}$ of convergent covers which appears in positive topologies. The main motivation of this paper is to construct the concrete categories $\text{rsfs}\text{C}\text{-}\mathbf{C}\mathbf{C}\mathbf{o}\mathbf{v}$, \ of\ $\mathbf{C}\mathbf{C}\mathbf{o}\mathbf{v}\text{-spaces}$, and $\mathbf{I}\text{-}\mathbf{C}Cov$, \ of\ $\mathbf{C}\mathbf{C}\mathbf{o}\mathbf{v}\text{-spaces}$ and deduce that they are topological categories.