2 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…