MathDB

Let

S

be the Sierpiński triangle. What can we say about the Hausdorff dimension of the elevation sets

f^{-1}(y)

for typical continuous real functions defined on

S

? (A property is satisfied for typical continuous real functions on

S

if the set of functions not having this property is of the first Baire category in the metric space of continuous

S\rightarrow\mathbb{R}

functions with the supremum norm.)
(translated by Miklós Maróti)

Problem Statement