On convergence structures in infinite graphs

2025/10/07 by Junior, Paulo Sérgio Farias Magalhães, Mezabarba, Renan Maneli, Monteiro, Rodrigo Santos
#Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2510.06336

Abstract

It is well known that a graph admits a natural closure operator defined on its vertex set, which also corresponds to a pretopology. In this paper, we describe the classical pretopology on a graph in terms of nets, with the aim of relating combinatorial properties to convergence properties.

Citations

• Abstract Integration in Net Convergence Structures
• On connected subsets of a convergence space
• Labeled Trees Generating Separable and Locally Finite Ultrametrics
• Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces
• A net theoretic approach to homotopy theory
• The directed Vietoris-Rips complex and homotopy and singular homology groups of finite digraphs

Related

• Net convergence structures with applications to vector lattices
• A net theoretic approach to homotopy theory
• Limit for Quotient Convergent Graph Sequence
• Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces
• On limits of finite graphs