A short proof of nonhomogeneity of the pseudo-circle

TL;DR

This paper presents a concise alternative proof demonstrating the nonhomogeneity of the pseudo-circle, building on recent results by Bellamy and Lewis, simplifying previous complex proofs.

Contribution

It offers a significantly shorter proof of the pseudo-circle's nonhomogeneity, improving understanding and accessibility of this topological property.

Findings

The pseudo-circle is nonhomogeneous.

The proof is shorter and more straightforward.

It relies on recent results by Bellamy and Lewis.

Abstract

The pseudo-circle is known to be nonhomogeneous. The original proofs of this fact were discovered independently by L. Fearnley and J.T. Rogers, Jr. The purpose of this paper is to provide an alternative, very short proof based on a result of D. Bellamy and W. Lewis.