A super-multiplicative inequality for the number of finite unlabeled arbitrary and $T_0$ topologies

Ibtsam A. R. Alroily, Brahim Chaourar

Let $n$ be a nonnegative integer, and $f(n)$ the number of unlabeled finite topologies on $n$ points. We prove that $f(n+m)\ge f(n)f(m)$ both for the labeled and unlabeled cases…