A metric property of Sierpiński hypercubes

Original Articles

A metric property of Sierpiński hypercubes

Published in: Quaestiones Mathematicae
Volume 36 , issue 2 , 2013 , pages: 197–208
DOI: 10.2989/16073606.2013.801141
Author(s): Heiko Hoffmann Department of Mathemactics, Germany
Keywords: Sierpiński hypercube , Sierpiński carpet , rectifiably connected , geodesic metric , shortest path distance , uniformly regular , quasi-convex , Sierpiński hypercube , Sierpiński carpet , rectifiably connected , geodesic metric , shortest path distance , uniformly regular , quasi-convex
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Abstract

In this short note we are engaged with sets we call generalized Sierpiński 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.
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