Geodesic
Method for constructing one-point expansions of a topology on a finite set and its applications
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2010), pp. 67-76 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 $X$. 
@article{BASM_2010_3_a7,
     author = {V. I. Arnautov and A. V. Kochina},
     title = {Method for constructing one-point expansions of a~topology on a~finite set and its applications},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {67--76},
     year = {2010},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2010_3_a7/}
}
TY  - JOUR
AU  - V. I. Arnautov
AU  - A. V. Kochina
TI  - Method for constructing one-point expansions of a topology on a finite set and its applications
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2010
SP  - 67
EP  - 76
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/BASM_2010_3_a7/
LA  - en
ID  - BASM_2010_3_a7
ER  - 
%0 Journal Article
%A V. I. Arnautov
%A A. V. Kochina
%T Method for constructing one-point expansions of a topology on a finite set and its applications
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2010
%P 67-76
%N 3
%U http://geodesic.mathdoc.fr/item/BASM_2010_3_a7/
%G en
%F BASM_2010_3_a7
V. I. Arnautov; A. V. Kochina. Method for constructing one-point expansions of a topology on a finite set and its applications. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2010), pp. 67-76. http://geodesic.mathdoc.fr/item/BASM_2010_3_a7/

[1] Gustavo N., Rubisno O., “Sobre el numero de topologias en un conjunto finito”, Boletin de Matematicas. Nueva Serie, 13:2 (2006), 136–158 | MR | Zbl

[2] The on-Line Encyclopedia of Integer Sequences!, number of topologies http://www.research.att.com

[3] Birkhoff G., The Theory of lattices, Nauka, Moscow, 1984 (Russian) | MR