# Cubical Covers of Sets in $\mathbb{R}^n$

## TL;DR

This paper explores the use of cubical coverings to understand wild sets in Euclidean space, examining their effectiveness and connections to geometric measure theory concepts like Jones' beta numbers and varifolds.

## Contribution

It introduces a focus on the wildest sets for which cubical coverings and related representations accurately reflect the original set's features.

## Key findings

- Identifies classes of wild sets well-represented by cubical covers
- Connects cubical coverings with Jones' beta numbers and varifolds
- Stimulates further research in geometric measure theory applications

## Abstract

Wild sets in $\mathbb{R}^n$ can be tamed through the use of various representations though sometimes this taming removes features considered important. Finding the wildest sets for which it is still true that the representations faithfully inform us about the original set is the focus of this rather playful, expository paper that we hope will stimulate interest in cubical coverings as well as the other two ideas we explore briefly: Jones' $\beta$ numbers and varifolds from geometric measure theory.