Devil's staircases, ramps, humps and roller coasters
Everywhere divergent Fourier series
Smooth Cantor functions
We characterise the set on which an infinitely differentiable function can be locally polynomial.
Hausdorff dimension of sums of sets with themselves
There is no non-trivial constraint on the Hausdorff dimension of sums of a set with itself.
Besicovitch via Baire
We construct various Besicovitch sets using Baire category arguments.
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