Classification of topologies on finite sets using graphs
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.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 7, pp 1164-1167.
Citation Example: Adamenko N. P., Velichko I. G. Classification of topologies on finite sets using graphs // Ukr. Mat. Zh. - 2008. - 60, № 7. - pp. 992–996.