Geodesic
On the number of topologies on countable skew fields
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2020), pp. 63-74 
V. I. Arnautov; G. N. Ermakova. On the number of topologies on countable skew fields. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2020), pp. 63-74. http://geodesic.mathdoc.fr/item/BASM_2020_1_a3/
@article{BASM_2020_1_a3,
     author = {V. I. Arnautov and G. N. Ermakova},
     title = {On the number of topologies on countable skew fields},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {63--74},
     year = {2020},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2020_1_a3/}
}
TY  - JOUR
AU  - V. I. Arnautov
AU  - G. N. Ermakova
TI  - On the number of topologies on countable skew fields
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2020
SP  - 63
EP  - 74
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BASM_2020_1_a3/
LA  - en
ID  - BASM_2020_1_a3
ER  - 
%0 Journal Article
%A V. I. Arnautov
%A G. N. Ermakova
%T On the number of topologies on countable skew fields
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2020
%P 63-74
%N 1
%U http://geodesic.mathdoc.fr/item/BASM_2020_1_a3/
%G en
%F BASM_2020_1_a3

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

If a countable skew field $ R $ admits a non-discrete metrizable topology $ \tau _0 $, then the lattice of all topologies of this skew fields admits: – Continuum of non-discrete metrizable topologies of the skew fields stronger than the topology $ \tau _0 $ and such that $ \sup \{\tau _1, \tau _2 \} $ is the discrete topology for any different topologies $ \tau_1$ and $\tau _2 $; – Continuum of non-discrete metrizable topologies of the skew fields stronger than $ \tau _0 $ and such that any two of these topologies are comparable; – Two to the power of continuum of topologies of the skew fields stronger than $ \tau _0 $, each of them is a coatom in the lattice of all topologies of the skew fields.

[1] Markov A.A., “On absolutely closed sets”, Mat. Sb., 18 (1945), 3–28 (in Russian)

[2] Arnautov V. I., Glavatsky S. T., Mikhalev A. V., Introduction to the topological rings and modules, Marcel Dekker, Inc., New York–Basel–Hong Kong, 1996 | MR | Zbl

[3] Arnautov V. I., “Non-discrete topologizability of countable rings”, DAN SSSR, 191 (1970), 747–750 (in Russian) | MR | Zbl

[4] Arnautov V. I., Ermakova G. N., “On the number of metrizable group topologies on countable groups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2013, no. 2(72)–3(73), 17–26 | MR | Zbl

[5] Arnautov V. I., Ermakova G. N., “On the number of group topologies on countable groups”, Bul. Acad. Ştiinţe Repub. Mold., Mat., 2014, no. 1(74), 101–112 | MR | Zbl

[6] Arnautov V. I., Ermakova G. N., “On the number of ring topologies on countable rings”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 1(77), 103–114 | MR | Zbl

[7] Arnautov V. I., Ermakova G. N., “On the number of topologies on countable fields”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 1(89), 79–90 | MR | Zbl