# Subgroups of $\mathbb{R}$-factorizable groups

Constancio Hernández; Mihail G. Tkachenko

Commentationes Mathematicae Universitatis Carolinae (1998)

- Volume: 39, Issue: 2, page 371-378
- ISSN: 0010-2628

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topHernández, 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 -

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