For citation:
Sultanov S. R. On a Quotient Topology in Topological Semigroups and Groups. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 4, pp. 422-424. DOI: 10.18500/1816-9791-2016-16-4-422-424, EDN: XHPYHX
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
14.11.2016
Full text:
(downloads: 164)
Language:
Russian
Heading:
UDC:
512.546
EDN:
XHPYHX
On a Quotient Topology in Topological Semigroups and Groups
Autors:
Sultanov Sergei Rezhepovich, Ryazan State University S. A. Esenin, Russia
Abstract:
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.
Key words:
References:
- Kargapolov M. E., Merzlyakov U. E. Osnovy teorii grupp [Basics of group theory]. Мosсow, Nauka, 1982. 288 p. (in Russian).
- Engelking R. Obshchaia topologiia [General topology]. Мoscow, Mir, 1986. 752 p. (in Russian).
- Pontryagin L. S. Nepreryvnye gruppy [Continuous groups]. Мosсow, Nauka, 1984. 520 p. (in Russian).
Received:
19.07.2016
Accepted:
29.10.2016
Published:
30.11.2016
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