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Existence of a continuous function

Source: 2022 Miklós Schweitzer Problem 10

November 12, 2022
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Problem Statement

Is there a continuous function f:R\Q→R\Qf : \mathbb R \backslash \mathbb Q \to \mathbb R \backslash \mathbb Q for which the archetype of every irrational number has a positive Hausdorff dimension?
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