Universal end-compactifications of locally finite graphs

TL;DR

This paper constructs a specific locally finite connected graph whose Freudenthal compactification serves as a universal space for all completely regular continua, including thin or graph-like continua.

Contribution

It introduces a universal end-compactification for locally finite graphs that encompasses all completely regular continua.

Findings

The constructed graph's Freudenthal compactification is universal for the class of completely regular continua.

The work links graph theory with continuum theory through a universal compactification.

Provides a new tool for studying the structure of complex continua via graph compactifications.

Abstract

We construct a locally finite connected graph whose Freudenthal compactification is universal for the class of completely regular continua, a class also known in the literature under the name thin or graph-like continua.