Reducing the upper bound for the Borsuk number in ${\mathbb{R}}^4$ to 8

Alexander Tolmachev, Vsevolod Voronov

The Borsuk number $b(n)$ of $n$-dimensional Euclidean space ${\mathbb{R}}^n$ is the smallest integer such that any set $F\subset {\mathbb{R}}^n$ of unit diameter can be partitioned in…