Separable Indecomposable Continuum with Exactly One Composant

TL;DR

This paper constructs a separable, indecomposable continuum with exactly one composant, demonstrating a non-metrizable yet 'small' example using Smith's method.

Contribution

It provides the first known example of a separable, indecomposable continuum with a single composant, expanding understanding of continuum theory.

Findings

Constructed a separable, indecomposable continuum with one composant

Demonstrated the existence of a 'small' non-metrizable continuum

Extended Smith's method to new class of continua

Abstract

Indecomposable continua with one composant are $\textit{large}$ in the sense of being non-metrisable. We adapt the method of Smith $[18]$ to construct an example which is $\textit{small}$ in the sense of being separable.