On the box dimension of subsets of a metric compact space
The question of possible values of the lower capacity dimension dimB of subsets of the metric compact set X is considered. The concept of dimension f dimBX is introduced, which characterizes the asymptotics of the lower capacity dimension of closed ε-neighborhoods of finite subsets of the compact set X for ε → 0 . For a wide class of metric compact sets, the dimension f dimBX is the same as dimBX . The following theorem is proved: for any non-negative number r < f dimBX there exists a closed subset Zr ⊂ X such that dimBZr = r.
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Keywords
metric compact space, capacitarian dimension, quantization dimension, intermediate value theorem for the capacitarian dimensionAuthors
| Name | Organization | |
| Ivanov Aleksandr V. | Karelian Scientific Center of Russian Academy of Sciences | alvlivanov@krc.karelia.ru |
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On the box dimension of subsets of a metric compact space | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2023. № 83. DOI: 10.17223/19988621/83/3
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