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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, Number 3, Pages 67–76 (Mi basm271)  

This article is cited in 2 scientific papers (total in 2 papers)

Research articles

Method for constructing one-point expansions of a topology on a finite set and its applications

V. I. Arnautova, A. V. Kochina

a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Abstract: The article consists of two parts. In the first part we present an algorithm which allows to receive, for any topology $\tau$ which is given on a set $X $ from $n$ elements, all topologies on the set $X\bigcup\{y\}$ each of which induces the topology $\tau$ on the set $X $. In the second part (as an example) this algorithm is applied for calculation of the number of topologies on the set $Y$ each of which induces the discrete topology on the set $X$.

Keywords and phrases: finite set, topologies, one-point expansions, lattice isomorphic.

Full text: PDF file (126 kB)
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Bibliographic databases:
MSC: 54A10
Received: 16.09.2010
Language:

Citation: V. I. Arnautov, A. V. Kochina, “Method for constructing one-point expansions of a topology on a finite set and its applications”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, no. 3, 67–76

Citation in format AMSBIB
\Bibitem{ArnKoc10}
\by V.~I.~Arnautov, A.~V.~Kochina
\paper Method for constructing one-point expansions of a~topology on a~finite set and its applications
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2010
\issue 3
\pages 67--76
\mathnet{http://mi.mathnet.ru/basm271}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2791978}
\zmath{https://zbmath.org/?q=an:1217.54003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Arnautov, “Estimation of the number of one-point expansions of a topology which is given on a finite set”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, no. 2, 17–22  mathnet  mathscinet  zmath
    2. V. I. Arnautov, “Method of construction of topologies on any finite set”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2, 29–42  mathnet  mathscinet  zmath
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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