Geodesic
Local theorems for topological groups
Izvestiya. Mathematics, Tome 15 (1980) no. 3, pp. 625-633 
I. V. Protasov. Local theorems for topological groups. Izvestiya. Mathematics, Tome 15 (1980) no. 3, pp. 625-633. http://geodesic.mathdoc.fr/item/IM2_1980_15_3_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Topological groups with various systems of closed invariant subgroups are studied, and theorems generalizing Mal'cev's local theorems for Kurosh–Chernikov class to locally compact groups are proved. As an application, information is obtained on systems of closed invariant subgroups of a locally compact, locally prosolvable or locally pronilpotent group. Problem 3.37 in the Kourovka notebook on the Frattini subgroup of a locally compact, locally pronilpotent group is also solved. A new topologization of the set of closed subsets of a topological space is applied to prove the local theorems. Bibliography: 9 titles.

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[5] Kourovskaya tetrad, Izdanie pyatoe, Novosibirsk, 1976

[6] Protasov I. V., “Zamknutye invariantnye podgruppy lokalno kompaktnykh grupp”, Dokl. AN SSSR, 239:5 (1978), 1060–1062 | MR | Zbl

[7] Kelli Dzh., Obschaya topologiya, Nauka, M., 1968

[8] Feli J. M. G., “A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space”, Proc. Amer. Math. Soc., 13:3 (1962), 472–476 | DOI | MR

[9] Kuratovskii K., Topologiya, I, Mir, M., 1966 | MR