Homogeneous continua that are not separated by arcs

TL;DR

This paper proves that in certain highly symmetric, locally homogeneous, and locally compact metric spaces, regions of dimension two cannot be separated by arcs, highlighting a topological property of such spaces.

Contribution

It establishes a new separation property for two-dimensional regions in strongly locally homogeneous, locally compact metric spaces, extending understanding of their topological structure.

Findings

Two-dimensional regions in the specified spaces are not separated by arcs.

The result applies to strongly locally homogeneous and locally compact spaces.

Provides insight into the topological behavior of high-symmetry continua.

Abstract

We prove that if $X$ is a strongly locally homogeneous and locally compact separable metric space and $G$ is a region in $X$ with $\dim G=2$, then $G$ is not separated by any arc in $G$.