A note on O. Frolkina's paper "Pairwise disjoint Moebius bands in space"

TL;DR

This paper provides a straightforward algebraic proof confirming that uncountably many pairwise disjoint Möbius bands cannot exist in three-dimensional space, extending the result to higher dimensions.

Contribution

It offers a simple algebraic proof of Frolkina's result and generalizes it to higher-dimensional spaces.

Findings

Uncountably many disjoint Möbius bands cannot exist in -dimensional space.

The proof extends to higher dimensions.

Simplifies the understanding of the spatial arrangement of Möbius bands.

Abstract

We note a simple algebraic proof of Frolkina's result that $\mathbb R^3$ does not contain uncountably many pairwise disjoint copies of the M\"obius band, and of a similar result in higher dimensions.