Closure and Interior Operators of the Category of Positive Topologies

2022/09/01 by Joaquı́n Luna-Torres, Luna-Torres, Joaquín
Computer Science · Mathematics · #03F65 #06A15 #06B23 #06D22 #Category Theory (math.CT) #Distributed and Parallel Computing Systems #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2209.00161

openalex publication_date 2022/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Interior Operators and Topological Categories
• Proper and admissible topologies in the setting of closure spaces
• Cartesian closed exact completions in topology
• Interpreter fr topologists
• Each closure operator induces a topology and vice-versa ("version for children")