Closure and Interior Operators of the Category of Positive Topologies

Abstract

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