Closure and Interior Operators of the Category of Positive Topologies

TL;DR

This paper introduces closure and interior operators within the category of convergent covers in positive topologies, aiming to construct and analyze related concrete categories and their topological properties.

Contribution

It defines and studies closure and interior operators in the category of convergent covers, and constructs associated concrete categories demonstrating their topological nature.

Findings

Defined closure and interior operators for convergent covers

Constructed concrete categories of CCov-spaces

Proved these categories are topological

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.