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On Lipschitz maps and dimension
-
Irmina Herburt
and
Roman Pol
Published/Copyright:
March 29, 2013
Abstract
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
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- On the counting of holomorphic discs in toric Fano manifolds
- Secant degree of toric surfaces and delightful planar toric degenerations
- Fractal curvature measures of self-similar sets
- On Lipschitz maps and dimension
- Solvsolitons associated with graphs
- On the Hessian geometry of a real polynomial hyperbolic near infinity
- Permutation polynomials and translation planes of even order
- On the derivative cones of polyhedral cones
- The conjugacy classes of finite nonsolvable subgroups in the plane Cremona group
- Gradient estimates for the p-Laplace heat equation under the Ricci flow
- The automorphism group of the generalized Giulietti–Korchmáros function field
