J. Integer Seq. 13(3), Article ID 10.3.5, 19 p., electronic only (2010)
Summary
Summary: Let $E$ be a set with $n$ elements, and let $T(n,k)$ be the number of all labeled topologies having $k$ open sets that can be defined on $E$. In this paper, we compute these numbers for $k \le 17$, and arbitrary $n$, as well as $t_{N0}(n,k)$, the number of all unlabeled non-$T_{0}$ topologies on $E$ with $k$ open sets, for $3 \le k \le 8$.
