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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, Number 2, Pages 29–42 (Mi basm319)  

Method of construction of topologies on any finite set

V. I. Arnautov

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

Abstract: Let a topology $\tau$ be defined on a finite set. We give the definition of quasiatoms in the lattice $(\tau,\subseteq)$ and study their properties. For any splitting of a finite set $X$ into $k$ subsets we give a method of constructing any topology on the set $X$ for which this splitting is the set of all quasiatoms and the weight of this topological space is equal to $k$.

Keywords and phrases: finite set, topologies, lattice of all open sets, atoms, quasiatoms.

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Document Type: Article
MSC: 54A10
Received: 24.05.2012
Revised: 21.09.2012
Language: English

Citation: V. I. Arnautov, “Method of construction of topologies on any finite set”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2, 29–42

Citation in format AMSBIB
\Bibitem{Arn12}
\by V.~I.~Arnautov
\paper Method of construction of topologies on any finite set
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2012
\issue 2
\pages 29--42
\mathnet{http://mi.mathnet.ru/basm319}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3060800}
\zmath{https://zbmath.org/?q=an:06179494}


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