Geodesic
Strongly countable-dimensional resolvents of sigma-compact groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 1, pp. 101-108.

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For every topological group $H$ which is a $Q^\infty$-manifold there exists a topological group which is an $\mathbb R^\infty$-manifold and can be mapped onto $H$ by a homomorphism satisfying some sufficiently strong softness conditions. 
@article{FPM_1998_4_1_a6,
     author = {M. M. Zarichnyi},
     title = {Strongly countable-dimensional resolvents of sigma-compact groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {101--108},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_1_a6/}
}
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M. M. Zarichnyi. Strongly countable-dimensional resolvents of sigma-compact groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 1, pp. 101-108. http://geodesic.mathdoc.fr/item/FPM_1998_4_1_a6/