Geodesic
On a quotient topology in topological semigroups and groups
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 4, pp. 422-424.

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The paper discusses the definution of the topological factor semigrop using the open congruence relations on this topological semigroup. Based on this approach, a description of all open gomomorfic images of topological semigroup is obtained. Similarly, this approach is used to describe all open homomorphic images of a topological group. 
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S. R. Sultanov. On a quotient topology in topological semigroups and groups. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 4, pp. 422-424. http://geodesic.mathdoc.fr/item/ISU_2016_16_4_a6/

[1] Kargapolov M. E., Merzlyakov U. E., Basics of group theory, Nauka, M., 1982, 288 pp. (in Russian) | MR

[2] Engelking R., General topology, Mir, M., 1986, 752 pp. (in Russian) | MR

[3] Pontryagin L. S., Continuous groups, Nauka, M., 1984, 520 pp. (in Russian) | MR