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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J. W. Evans, F. Harary, and M. S. Lynn, “On the computer enumeration of finite topologies,” Commun. ASM, 10, 295–298 (1967).
V. P. Kozyrev, “Enumeration of transitive oriented graphs and imbedding of transitive graphs,” Vopr. Kibern., Issue 15, 44–60 (1975).
V. A. Gorbatov, Foundations of Discrete Mathematics [in Russian], Vysshaya Shkola, Moscow (1986).
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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