All Questions

Fix a real number $0\leq t\leq 1$ and an integer $n>1$. Let $\mathbb{S}^{n-1}\subset\mathbb{R}^n$ denote the unit hypersphere. Define $$d_N(n;t):=\max\sum_{i<j}\Vert P_i-P_j\Vert_2^t$$ where ...

Recall that a plane continuum is a closed, bounded, connected subset of the plane. It is non-degenerate if it contains at least two points. (We may sometimes just say "continuum" even if we ...