Geodesic
Certain discreteness conditions imposed on topological groups
Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 437-442.

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The paper studies locally compact groups in which any closed subset generates, in the algebraic sense, a subgroup which is closed. It is proven that all such groups are discrete. 
@article{MZM_1973_13_3_a13,
     author = {V. M. Poletskikh},
     title = {Certain discreteness conditions imposed on topological groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {437--442},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a13/}
}
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V. M. Poletskikh. Certain discreteness conditions imposed on topological groups. Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 437-442. http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a13/