A metric property of Sierpinski hypercubes

Abstract

In this short note we are engaged with sets we call generalized Sierpinski hypercubes. We give a detailed proof of the fact that these sets are uniformly regular, i.e., the geodesic metric is comparable to the Euclidean one.

Keywords: Sierpinski hypercube, Sierpinski carpet, rectifiably connected, geodesic metric, shortest path distance, uniformly regular, quasi-convex

Quaestiones Mathematicae 36(2013), 197–208