A new fractal dimension: The topological Hausdorff dimension |
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| Authors: | Richá rd Balka,Zoltá n Buczolich,Má rton Elekes |
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| Affiliation: | 1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, PO Box 127, 1364 Budapest, Hungary;2. Institute of Mathematics and Informatics, Eszterházy Károly College, Leányka u. 4., 3300 Eger, Hungary;3. Institute of Mathematics, Eötvös Loránd University, Pázmány Péter s. 1/c, 1117 Budapest, Hungary |
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| Abstract: | We introduce a new concept of dimension for metric spaces, the so-called topological Hausdorff dimension. It is defined by a very natural combination of the definitions of the topological dimension and the Hausdorff dimension. The value of the topological Hausdorff dimension is always between the topological dimension and the Hausdorff dimension, in particular, this new dimension is a non-trivial lower estimate for the Hausdorff dimension. |
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| Keywords: | primary, 28A78, 28A80 secondary, 54F45, 60J65, 60K35 |
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