Geodesic
Topological groups in which each nowhere dense subset is closed
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 207-211

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Assuming the validity of the combinatorial principle $p=\mathfrak C$, which follows from Martin's axiom, it is proved that an arbitrary nondiscrete metrizable group topology on an Abelian group can be strengthened to a nondiscrete group topology in which each nowhere dense subset is closed. 
@article{MZM_1998_64_2_a5,
     author = {E. G. Zelenyuk},
     title = {Topological groups in which each nowhere dense subset is closed},
     journal = {Matemati\v{c}eskie zametki},
     pages = {207--211},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a5/}
}
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E. G. Zelenyuk. Topological groups in which each nowhere dense subset is closed. Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 207-211. http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a5/