Cubical Covers of Sets in R^n

Abstract

Wild sets in 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 wild sets and their representations, as well as the other two ideas we explore very briefly: Jones' β numbers and varifolds from geometric measure theory.