Accessible Requires Authentication Published by De Gruyter March 29, 2013

On Lipschitz maps and dimension

Irmina Herburt and Roman Pol
From the journal


Maria Moszyńska and the first author suggested some natural axioms for fractal dimension functions. We discuss the independence of these axioms. In particular, using the Continuum Hypothesis, we associate to each nonempty separable metric space X a non-negative integer d(X) so that the function d is Lipschitz subinvariant, stable under finite unions, d([0; 1]n) = n, but still, for some E ⊂ [0; 1]3 we have d(E) < dimE, where dimE is the topological dimension of E.

Published Online: 2013-03-29
Published in Print: 2013-04

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