Geodesic
Free topological algebra with separately continuous Mal'tsev operation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 89-99.

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

Topological spaces with separately continuous Mal'tsev operation, called quasi-Mal'tsev spaces, are considered. The existence of the free quasi-Mal'tsev space generated by an arbitrary completely regular Hausdorff space is proved. It is shown that any quasi-Mal'tsev space is a quotient of a free quasi-Mal'tsev space. It is also shown that the topology of a free quasi-Mal'tsev space has a simple and natural description in terms of the generating space. Finally, it is proved that any completely regular Hausdorff quasi-Mal'tsev space is a retract of a quasi-topological group.
Keywords: Mal'tsev operation, free quasi-Mal'tsev space, quasi-topological group.
Mots-clés : quasi-Mal'tsev space 
@article{FAA_2023_57_4_a6,
     author = {O. V. Sipacheva and A. A. Solonkov},
     title = {Free topological algebra with separately continuous {Mal'tsev} operation},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {89--99},
     publisher = {mathdoc},
     volume = {57},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a6/}
}
TY  - JOUR
AU  - O. V. Sipacheva
AU  - A. A. Solonkov
TI  - Free topological algebra with separately continuous Mal'tsev operation
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2023
SP  - 89
EP  - 99
VL  - 57
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a6/
LA  - ru
ID  - FAA_2023_57_4_a6
ER  - 
%0 Journal Article
%A O. V. Sipacheva
%A A. A. Solonkov
%T Free topological algebra with separately continuous Mal'tsev operation
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2023
%P 89-99
%V 57
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a6/
%G ru
%F FAA_2023_57_4_a6
O. V. Sipacheva; A. A. Solonkov. Free topological algebra with separately continuous Mal'tsev operation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 89-99. http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a6/

[1] A. I. Maltsev, “K obschei teorii algebraicheskikh sistem”, Matem. sb., 35(77):1 (1954), 3–20 | Zbl

[2] A. I. Maltsev, “Svobodnye topologicheskie algebry”, Izv. AN SSSR. Ser. matem., 21:2 (1957), 171–198 | Zbl

[3] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970 | MR

[4] Obschaya algebra, v. 2, ed. pod obsch. red. L. A. Skornyakova, Nauka. Gl. red. fiz.-mat. lit., M., 1991

[5] O. V. Sipacheva, “Kompakty s nepreryvnoi operatsiei Maltseva i retrakty topologicheskikh grupp”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1991, no. 1, 33–36 | MR | Zbl

[6] V. V. Uspenskii, “O nepreryvnykh obrazakh lindelefovykh topologicheskikh grupp”, Dokl. AN SSSR, 285:4 (1985), 824–827 | MR | Zbl

[7] V. V. Uspenskii, “Retrakty topologicheskikh grupp i kompakty Dugundzhi”, Topologiya i ee prilozheniya, Tr. MIAN SSSR, 193, Nauka, M., 1992, 192–196

[8] M. M. Choban, “K teorii topologicheskikh algebraicheskikh sistem”, Tr. MMO, 48 (1985), 106–149, Izdatelstvo Moskovskogo universiteta, M.

[9] R. Engelking, Obschaya topologiya, Mir, M., 1986

[10] J. Brazas, S. Emery, “Free Quasitopological Groups”, Topology Appl., 326 (2023), 108416 | DOI | MR | Zbl

[11] P. M. Gartside, E. A. Reznichenko, O. V. Sipacheva, “Mal'tsev and retral spaces”, Topology Appl., 80:1–2 (1997), 115–129 | DOI | MR | Zbl

[12] E. A. Reznichenko, V. V. Uspenskij, “Pseudocompact Mal'tsev spaces”, Topology Appl., 86:1 (1998), 83–104 | DOI | MR | Zbl

[13] S. Świerczkowski, “Topologies on free algebras”, Proc. London Math. Soc., 14:3 (1964), 566–576 | DOI | MR | Zbl

[14] V. V. Uspenskii, “The Mal'tsev operation on countably compact spaces”, Comment. Math. Univ. Carolinae, 30:2 (1989), 395–402 | MR | Zbl