From continua to R-trees

TL;DR

This paper introduces methods to construct R-trees from continua by using cut points and cut pairs, providing a new way to analyze their topological structure.

Contribution

It presents novel techniques for associating R-trees with continua based on their cut points and cut pairs, expanding the tools for topological analysis.

Findings

R-trees can be associated with continua via cut points

R-trees can be constructed from cut pairs in continua without cut points

Provides a new perspective on the topological structure of continua

Abstract

We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X.