On the Number of Distinct Topological Bases of a Finite Set of Size $N$

Lars Warren Ericson

For a finite set $S$ with $|S|=N$, the number of families $\mathcal{B}\subseteq \mathcal{P}(S)$ that are topological bases is $\#(N) = \sum_{\mathcal{T} \in \operator…