On the number of finite topological spaces

Abstract

In this paper we deal with the problem of enumerating the finite topological spaces, studying the enumeration of a restrictive class of them. By employing simple techniques, we obtain a recursive lower bound for the number of topological spaces on a set of n elements. Besides we prove some collateral results, among which we can bring a new proof (Cor. 1.5) of the fact that p(n) – the number of partitions of the integer n – is the number of non-isomorphic Boolean algebras on a set of n elements.