Characterization of the $n$-dimensional Sierpi\'nski carpet as an inverse limit of closed balls

TL;DR

This paper extends a theorem characterizing the n-dimensional Sierpiński carpet as an inverse limit of closed balls, generalizing previous results to higher dimensions.

Contribution

It generalizes a known theorem to characterize the n-dimensional Sierpiński carpet as an inverse limit of closed balls for any dimension.

Findings

The Sierpiński carpet can be represented as an inverse limit of closed balls in any dimension.

The generalization applies the theorem of Tshishiku and Walsh to higher dimensions.

Provides a new framework for understanding fractal structures in topology.

Abstract

In this paper we generalize, for any dimension, a theorem of Tshishiku and Walsh that characterizes the Sierpi\'nski carpet as a limit set of maps from the disc to the sphere.