Том 71
№ 11

All Issues

Adamenko N. P.

Articles: 1
Brief Communications (Russian)

Classification of topologies on finite sets using graphs

Adamenko N. P., Velichko I. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 7. - pp. 992–996

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.