Classification of topologies on finite sets using graphs |
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Authors: | N P Adamenko I G Velichko |
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Institution: | (1) Zaporozhye National University, Zaporozhye, Ukraine |
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Abstract: | 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.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 992–996, July, 2008. |
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Keywords: | |
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