Subgroups of $ℝ$-factorizable groups

Hernández, Constancio, and Tkachenko, Mihail G.. "Subgroups of $\mathbb {R}$-factorizable groups." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 371-378. <http://eudml.org/doc/22345>.

@article{Hernández1998,
abstract = {The properties of $\mathbb \{R\}$-factorizable groups and their subgroups are studied. We show that a locally compact group $G$ is $\mathbb \{R\}$-factorizable if and only if $G$ is $\sigma $-compact. It is proved that a subgroup $H$ of an $\mathbb \{R\}$-factorizable group $G$ is $\mathbb \{R\}$-factorizable if and only if $H$ is $z$-embedded in $G$. Therefore, a subgroup of an $\mathbb \{R\}$-factorizable group need not be $\mathbb \{R\}$-factorizable, and we present a method for constructing non-$\mathbb \{R\}$-factorizable dense subgroups of a special class of $\mathbb \{R\}$-factorizable groups. Finally, we construct a closed $G_\{\delta \}$-subgroup of an $\mathbb \{R\}$-factorizable group which is not $\mathbb \{R\}$-factorizable.},
author = {Hernández, Constancio, Tkachenko, Mihail G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\mathbb \{R\}$-factorizable group; $z$-embedded set; $\aleph _0$-bounded group; $P$-group; Lindelöf group; -space; -group; pseudo--compact; -stable; -factorizable},
language = {eng},
number = {2},
pages = {371-378},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Subgroups of $\mathbb \{R\}$-factorizable groups},
url = {http://eudml.org/doc/22345},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Hernández, Constancio
AU - Tkachenko, Mihail G.
TI - Subgroups of $\mathbb {R}$-factorizable groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 371
EP - 378
AB - The properties of $\mathbb {R}$-factorizable groups and their subgroups are studied. We show that a locally compact group $G$ is $\mathbb {R}$-factorizable if and only if $G$ is $\sigma $-compact. It is proved that a subgroup $H$ of an $\mathbb {R}$-factorizable group $G$ is $\mathbb {R}$-factorizable if and only if $H$ is $z$-embedded in $G$. Therefore, a subgroup of an $\mathbb {R}$-factorizable group need not be $\mathbb {R}$-factorizable, and we present a method for constructing non-$\mathbb {R}$-factorizable dense subgroups of a special class of $\mathbb {R}$-factorizable groups. Finally, we construct a closed $G_{\delta }$-subgroup of an $\mathbb {R}$-factorizable group which is not $\mathbb {R}$-factorizable.
LA - eng
KW - $\mathbb {R}$-factorizable group; $z$-embedded set; $\aleph _0$-bounded group; $P$-group; Lindelöf group; -space; -group; pseudo--compact; -stable; -factorizable
UR - http://eudml.org/doc/22345
ER -