arXiv subjects

Joaquín Luna-Torres

Publications and source records attributed to Joaquín Luna-Torres.

2 recordsLinked to original sources

arXiv2023

Closure and Interior Operators of the Category of Positive Topologies

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.

math.CT↗

arXiv2021

Filters and compactness on small categories and locales

In analogy with the classical theory of filters, for fi\-nite\-ly complete or small cat\-e\-go\-ries, we provide the concepts of fil\-ter, $\mathfrak{G}$-neigh\-bor\-hood (short for "Grothendieck-neigh\-bor\-hood") and cover-neigh\-bor\-hood of points of such categories, with the goal of studying convergence, cluster point, closure of sieves and compactness on objects of that kind of categories. Finally, we study all these concepts in the category $\bf{Loc}$ of locales.

math.CT↗