Geodesic
Subgroups of $\Bbb R$-factorizable groups
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 371-378.

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The properties of $\Bbb R$-factorizable groups and their subgroups are studied. We show that a locally compact group $G$ is $\Bbb R$-factorizable if and only if $G$ is $\sigma$-compact. It is proved that a subgroup $H$ of an $\Bbb R$-factorizable group $G$ is $\Bbb R$-factorizable if and only if $H$ is $z$-embedded in $G$. Therefore, a subgroup of an $\Bbb R$-factorizable group need not be $\Bbb R$-factorizable, and we present a method for constructing non-$\Bbb R$-factorizable dense subgroups of a special class of $\Bbb R$-factorizable groups. Finally, we construct a closed $G_{\delta}$-subgroup of an $\Bbb R$-fac\-torizable group which is not $\Bbb R$-factorizable.
Classification : 22A05, 22D05, 54C50, 54H11
Keywords: $\Bbb R$-factorizable group; $z$-embedded set; $\aleph_0$-bounded group; $P$-group; Lindelöf group 
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     title = {Subgroups of $\Bbb R$-factorizable groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {371--378},
     publisher = {mathdoc},
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Hernández, Constancio; Tkačenko, Michael. Subgroups of $\Bbb R$-factorizable groups. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 371-378. http://geodesic.mathdoc.fr/item/CMUC_1998__39_2_a13/