The groups $S^3$ and $SO(3)$ have no invariant binary $k$-network

Taras Banakh, Slawomir Turek

A family $\mathcal{N}$ of closed subsets of a topological space $X$ is called a {\em closed $k$-network} if for each open set $U\subset X$ and a compact subset $K\subset U$ there is…