Geodesic
Method of construction of topologies on any finite set
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 29-42 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $k$. 
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     author = {V. I. Arnautov},
     title = {Method of construction of topologies on any finite set},
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V. I. Arnautov. Method of construction of topologies on any finite set. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 29-42. http://geodesic.mathdoc.fr/item/BASM_2012_2_a2/

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[2] Arnautov V. I., “Estimation of the number of one-point expansions of a topology which is given on a finite set”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2011, no. 2(65), 17–22 | MR | Zbl

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