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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, Number 2, Pages 17–22 (Mi basm285)  

This article is cited in 1 scientific paper (total in 1 paper)

Estimation of the number of one-point expansions of a topology which is given on a finite set

V. I. Arnautov

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

Abstract: Let $X$ be a finite set and $\tau$ be a topology on $X$ which has precisely $m$ open sets. If $t (\tau)$ is the number of possible one-point expansions of the topology $\tau$ on $Y=X\bigcup\{y\}$, then $\frac{m\cdot(m+3)}2-1\ge t(\tau)\ge2\cdot m+\log_2m-1$ and $\frac{m\cdot(m+3)}2-1=t(\tau)$ if and only if $\tau$ is a chain (i.e. it is a linearly ordered set) and $t(\tau)=2\cdot m+\log_2m-1$ if and only if $\tau$ is an atomistic lattice.

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

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Document Type: Article
MSC: 54A10
Received: 24.05.2011
Revised: 21.09.2011
Language: English

Citation: 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

Citation in format AMSBIB
\Bibitem{Arn11}
\by V.~I.~Arnautov
\paper Estimation of the number of one-point expansions of a~topology which is given on a~finite set
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2011
\issue 2
\pages 17--22
\mathnet{http://mi.mathnet.ru/basm285}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2895774}
\zmath{https://zbmath.org/?q=an:1244.54008}


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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, “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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