Inverse Limits and Topologies of Infinite Graphs

TL;DR

This paper explores the topologies of infinite graphs, particularly Etop and Itop, demonstrating that Itop can be constructed via inverse limits and applying this to build a topological spanning tree.

Contribution

It introduces a novel inverse limit construction for Itop topology and applies it to develop a topological spanning tree in infinite graphs.

Findings

Itop can be realized as an inverse limit of finite graphs.

A topological spanning tree can be constructed in Itop.

The paper characterizes Etop and Itop topologies for infinite graphs.

Abstract

Two of the natural topologies for infinite graphs with edge-ends are Etop and Itop. In this paper, we study and characterize them. We show that Itop can be constructed by inverse limits of inverse systems of graphs with finitely many vertices. Furthermore, as an application of the inverse limit approach, we construct a topological spanning tree in Itop