Iterated Brownian motion ad libitum is not the pseudo-arc

TL;DR

This paper demonstrates that a certain random continuum constructed from independent two-sided Brownian motions is almost surely indecomposable but not the pseudo-arc, clarifying its topological nature.

Contribution

It provides a rigorous proof that the constructed continuum is not the pseudo-arc, contrasting previous assumptions and expanding understanding of Brownian motion-based continua.

Findings

The continuum is almost surely indecomposable.

It is not the pseudo-arc.

The continuum is non-degenerate and not-hereditary indecomposable.

Abstract

We show that the construction of a random continuum $\mathcal{C}$ from independent two-sided Brownian motions as considered in arXiv:2004.01367 almost surely yields a non-degenerate indecomposable but not-hereditary indecomposable continuum. In particular $\mathcal{C}$ is (unfortunately) not the pseudo-arc.