5 problems

Let $U$ be a bounded open set in ${\mathbb R}^d$. Write $C(\overline U)$ for the space of continuous real-valued functions on $\overline U$, and let $G_\delta$ denote a countable i…

A unit speed curve is a curve parametrized by arclength, and a $C^1$ curve has a continuous first derivative. Existence conjecture. There is a continuous function … whose restricti…

The preceding Fourier-series calculations define the half-order fractional derivative $\frac{\mathrm{d}^{+\frac{1}{2}}}{\mathrm{d}x^{+\frac{1}{2}}}f(x)$, whose truncated Fourier se…

Weierstrass-type conjecture. The Fourier series above represents a function of the Weierstrass type that is continuous but nowhere differentiable.

For each integer $n e 0$, let $T{1/2,n}$ be the corresponding generalized Takagi function on $[0,1]$, and consider its points of absolute maximum. Allaart–Kawamura conjecture.…