Method of construction of topologies on any finite set
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 29-42.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let a topology τ be defined on a finite set. We give the definition of quasiatoms in the lattice (τ,) 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.
@article{BASM_2012_2_a2,
     author = {V. I. Arnautov},
     title = {Method of construction of topologies on any finite set},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {29--42},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a2/}
}
TY  - JOUR
AU  - V. I. Arnautov
TI  - Method of construction of topologies on any finite set
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2012
SP  - 29
EP  - 42
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a2/
LA  - en
ID  - BASM_2012_2_a2
ER  - 
%0 Journal Article
%A V. I. Arnautov
%T Method of construction of topologies on any finite set
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2012
%P 29-42
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a2/
%G en
%F BASM_2012_2_a2
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. https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a2/

[1] Arnautov V. I., Kochina A. V., “The method of construction of one-point expansions of a topology on a finite set and its application”, Bul. Acad. Ştiinţe Repub. Moldova. Mat., 2010, no. 3(64), 67–76 | MR | Zbl

[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

[3] Skornyakov L. A., Elements of the theory of structures, Nauka, Moscow, 1982 (in Russian) | MR | Zbl

[4] Birkgoff G., Theory of lattices, Nauka, Moscow, 1984 (in Russian)