The μ-topological Hausdorff dimension
In 2015, R. Balkaa, Z. Buczolich and M. Elekes introduced the topological Hausdorff 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 definiti...
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University of Extremadura
2019-12-01
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| Series: | Extracta Mathematicae |
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| Online Access: | https://publicaciones.unex.es/index.php/EM/article/view/65 |
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doaj-31616091c87e438b91aeabc2702e4d3f2021-02-02T17:21:38ZengUniversity of ExtremaduraExtracta Mathematicae0213-87432605-56862019-12-01342The μ-topological Hausdorff dimensionHela Lofti0Department of Mathematics, Faculty of Sciences of Monastir 5000-Monastir, Tunisia In 2015, R. Balkaa, Z. Buczolich and M. Elekes introduced the topological Hausdorff 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 Sierpiński 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 Sierpiński carpet coincides with the lower and upper bounds. https://publicaciones.unex.es/index.php/EM/article/view/65Hausdorff dimensionTopological Hausdorff dimension |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hela Lofti |
| spellingShingle |
Hela Lofti The μ-topological Hausdorff dimension Extracta Mathematicae Hausdorff dimension Topological Hausdorff dimension |
| author_facet |
Hela Lofti |
| author_sort |
Hela Lofti |
| title |
The μ-topological Hausdorff dimension |
| title_short |
The μ-topological Hausdorff dimension |
| title_full |
The μ-topological Hausdorff dimension |
| title_fullStr |
The μ-topological Hausdorff dimension |
| title_full_unstemmed |
The μ-topological Hausdorff dimension |
| title_sort |
μ-topological hausdorff dimension |
| publisher |
University of Extremadura |
| series |
Extracta Mathematicae |
| issn |
0213-8743 2605-5686 |
| publishDate |
2019-12-01 |
| description |
In 2015, R. Balkaa, Z. Buczolich and M. Elekes introduced the topological Hausdorff 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 Sierpiński 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 Sierpiński carpet coincides with the lower and upper bounds.
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| topic |
Hausdorff dimension Topological Hausdorff dimension |
| url |
https://publicaciones.unex.es/index.php/EM/article/view/65 |
| work_keys_str_mv |
AT helalofti themtopologicalhausdorffdimension AT helalofti mtopologicalhausdorffdimension |
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