With the use of directed graphs, we study topologies on finite sets. On this basis, we propose a new classification of these topologies. Some properties of T 0-topologies on finite sets are proved. In particular, we prove the existence, in T 0-topologies, of open sets containing any number of elements that does not exceed the cardinality of the set itself.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 992–996, July, 2008.
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Adamenko, N.P., Velichko, I.G. Classification of topologies on finite sets using graphs. Ukr Math J 60, 1164–1167 (2008). https://doi.org/10.1007/s11253-008-0113-9
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DOI: https://doi.org/10.1007/s11253-008-0113-9