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http://hdl.handle.net/10662/10325
Title: | The μ-topological Hausdoff dimension |
Authors: | Lotfi, Hela |
Keywords: | Hausdorff dimension;Topological Hausdorff dimension;Dimensión de Hausdorff;Dimensión topológica de Hausdorff |
Issue Date: | 2019 |
Publisher: | Universidad de Extremadura |
Abstract: | In 2015, R. Balkaa, Z. Buczolich and M. Elekes introduced the topological Hausdoff dimension which is a combination of the definitions of the topological dimension and the Hausdorff dimension. In our manuscript, we propose to generalize the topological Hausdorff dimension by combining the definitions of the topological dimension and the μ-Hausdorff dimension and we call it the μ-topological Hausdorff dimension. We will present upper and lower bounds for the μ-topological Hausdorff dimension of the Sierpinski carpet valid in a general framework. As an application, we give a large class of measures μ, where the μ-topological Hausdorff dimension of the Sierpinski carpet coincides with the lower and upper bounds. |
URI: | http://hdl.handle.net/10662/10325 |
DOI: | 10.17398/2605-5686.34.2.237 |
Appears in Collections: | Extracta Mathematicae Vol. 34, nº 2 (2019) |
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2605-5686_34_2_237.pdf | 357,71 kB | Adobe PDF | View/Open |
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