A recursive determination of topologies on finite sets (Q1346456)

The problem of enumeration of topologies on a finite set is studied by \textit{V. Krishnamurthy} [Am. Math. Mon. 73, 154-157 (1966; Zbl 0135.407)], \textit{K. H. Kim} [Boolean matrix theory and applications, Pure Appl. Math. Marcel Dekker 70 (1982; Zbl 0495.15003)] and others. In the present work we study a recursive determination of topologies on finite sets. Starting with a single topology on a singleton set, we can determine four topologies on a two element set which in turn can be used to obtain 29 topologies on a tripleton set. These 29 topologies can be used to derive 355 topologies on a set containing four elements and so on.