Please use this identifier to cite or link to this item: http://hdl.handle.net/10662/10325
Title: The μ-topological Hausdoff dimension
Authors: Lotfi, Hela
Université de Monastir. Tunisie
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
Appears in Collections:Extracta Mathematicae Vol. 34, nº 2 (2019)

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