Cite this article as:
Sultanov S. R. On a Quotient Topology in Topological Semigroups and Groups. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2016, vol. 16, iss. 4, pp. 422-424. DOI: https://doi.org/10.18500/1816-9791-2016-16-4-422-424
On a Quotient Topology in Topological Semigroups and Groups
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.
1. Kargapolov M. E., Merzlyakov U. E. Osnovy teorii grupp [Basics of group theory]. Мosсow, Nauka, 1982. 288 p. (in Russian).
2. Engelking R. Obshchaia topologiia [General topology]. Мoscow, Mir, 1986. 752 p. (in Russian).
3. Pontryagin L. S. Nepreryvnye gruppy [Continuous groups]. Мosсow, Nauka, 1984. 520 p. (in Russian).
