Classification of topologies on finite sets using graphs - Adamenko, N. P.; Velichko, I. G. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
With the use of digraphs, topologies on finite sets are studied. On this basis, a new classification of such topologies is proposed. Some properties of T0-topologies on finite sets are proved. In particular, it is proved that, in T0-topologies, there exist open sets containing arbitrary number of elements that does not exceed the cardinality of the set itself.