Hausdorff Dimension is onto

Karol Gryszka

Abstrakt


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?

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