On the fundamental group of $\mathbb R^3$ modulo the Case-Chamberlin continuum

TL;DR

This paper proves that the fundamental group of the quotient of three-dimensional space by the Case-Chamberlin continuum is uncountably infinite, extending previous knowledge of its nontriviality.

Contribution

It establishes that the fundamental group in this setting is uncountably infinite, a significant strengthening of prior results showing only nontriviality.

Findings

The fundamental group is nontrivial.

The fundamental group is uncountably infinite.

The result extends understanding of quotient spaces by complex continua.

Abstract

It has been known for a long time that the fundamental group of the quotient of $\RR ^3$ by the Case-Chamberlin continuum is nontrivial. In the present paper we prove that this group is in fact, uncountable.