Indecomposable Continuum with a Strong Non-Cut Point

TL;DR

This paper constructs a unique indecomposable continuum featuring exactly one strong non-cut point by adapting existing methods and using inverse limits of chains of continua.

Contribution

It introduces a novel construction of an indecomposable continuum with a single strong non-cut point, expanding the understanding of continuum topology.

Findings

Successfully constructs the continuum with the desired properties.

Demonstrates the method of using inverse limits and identifications.

Provides a new example in the study of indecomposable continua.

Abstract

We construct an indecomposable continuum with exactly one strong non-cut point. The method is an adaptation of Bellamy $[1]$. We start with an $\omega_1$-chain of indecomposable metric continua and retractions. The inverse limit is an indecomposable continuum with exactly two composants. Our example is formed by identifying a point in each composant.