3 papers
math.CO2026
On convergence structures in graphs
Paulo Magalhães Junior, Renan Maneli Mezabarba, Rodrigo Santos Monteiro
A closure operator on a set is a function satisfying, for all , the following properties: extensivity, $A \subseteq \op…
math.AT2024
Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces
Rodrigo Santos Monteiro
Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of expo…
math.AT2024
A net theoretic approach to homotopy theory
Renan Maneli Mezabarba, Rodrigo Santos Monteiro, Thales Fernando Vilamaior Paiva
This paper uses a net-theoretic approach to convergence spaces, aimed to simplify the description of continuous convergence in order to apply it in problems concerning Homotopy The…