All Questions

Let $\Omega \subset \mathbb R^3$ be a bounded regular simply connected domain contained in a ball $S$. Assume also that $\Omega$ is simply connected by surfaces (i.e. every regular closed surface ...

Let $f : [a,b] \to \Bbb R$ be everywhere differentiable with $f'(a) = 1$ and $f'(b) =-1$. By Darboux theorem, we know that $f'([a,b])$ is an interval containing $[-1,1]$. In particular, the set $\{x \...