Abstract: The aim of this article is to solve the following problem: given any positive real number $h$ construct a set $X$ such that its Hausdorff dimension is equal to $h$ . We obtain the result via generalized Cantor sets in arbitrary dimension.~We also discuss the following question : how many topologically different sets can have common Hausdorff dimension?
Publication Year: 2019
Publication Date: 2019-01-14
Language: en
Type: article
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Cited By Count: 3
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