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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 11, Pages 23–31 (Mi ivm9049)  
This article is cited in 3 scientific papers (total in 3 papers)

The listing of topologies close to the discrete one on finite sets

I. G. Velichkoa, P. G. Stegantsevab, N. P. Bashovab

a Chair of Higher Mathematics and Physics, Tavria State Agrotechnological University, 18 B. Khmelnitskogo Ave., Melitopol', Zaporozhye Region, 72310 Ukraine
b Chair of Algebra and Geometry, Zaporozhye National University, 66 Zhukovskogo str., Zaporozhye, 69600 Ukraine
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Abstract: We consider $T_0$-topologies on $n$-element set that contain more than $2^n$ elements. We solve a problem of listing and counting of such topologies. For this purpose we introduce the notions of an index of the topology and a vector of the topology. We study their properties and single out all possible classes of the topologies under the consideration. We formulate and prove a theorem related to the number of the topologies in each of the classes.
Keywords: topology on a finite set, $T_0$-topology, index of an element of a topology, index of a topology, vector of a topology.
Received: 19.03.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 11, Pages 19–25
DOI: https://doi.org/10.3103/S1066369X1511002X
Bibliographic databases:
Document Type: Article
UDC: 519.115
Language: Russian
Citation: I. G. Velichko, P. G. Stegantseva, N. P. Bashova, “The listing of topologies close to the discrete one on finite sets”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 11, 23–31; Russian Math. (Iz. VUZ), 59:11 (2015), 19–25
Citation in format AMSBIB
\Bibitem{VelSteBas15}
\by I.~G.~Velichko, P.~G.~Stegantseva, N.~P.~Bashova
\paper The listing of topologies close to the discrete one on finite sets
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 11
\pages 23--31
\mathnet{http://mi.mathnet.ru/ivm9049}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 11
\pages 19--25
\crossref{https://doi.org/10.3103/S1066369X1511002X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84945184402}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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