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→R functions with the supremum norm.)(translated by Miklós Maróti) Miklos Schweitzercollege conteststopologyfunction