Subgroups of $\Bbb R$-factorizable groups
Hernández, Constancio ; Tkachenko, Mihail G.
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 371-378 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1998-01-01
Classification:  22A05,  22D05,  54C50,  54H11 
@article{119014,
     author = {Constancio Hern\'andez and Mihail G. Tkachenko},
     title = {Subgroups of $\Bbb R$-factorizable groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {371-378},
     zbl = {1100.54026},
     mrnumber = {1651979},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119014}
}

Hernández, Constancio; Tkachenko, Mihail G. Subgroups of $\Bbb R$-factorizable groups. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 371-378. http://gdmltest.u-ga.fr/item/119014/

Comfort W.W. Compactness like properties for generalized weak topological sums, Pacific J. Math. 60 (1975), 31-37. (1975) | MR 0431088 | Zbl 0307.54016

Comfort W.W.; Ross K.A. Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (1966), 483-496. (1966) | MR 0207886 | Zbl 0214.28502

Guran I.I. On topological groups close to being Lindelöf, Soviet Math. Dokl. 23 (1981), 173-175. (1981) | Zbl 0478.22002

Hernández S.; Sanchiz M.; Tkačenko M. Bounded sets in spaces and topological groups, submitted for publication.

Engelking R. General Topology, Heldermann Verlag, 1989. | MR 1039321 | Zbl 0684.54001

Pontryagin L.S. Continuous Groups, Princeton Univ. Press, Princeton, 1939. | Zbl 0659.22001

Tkačenko M.G. Subgroups, quotient groups and products of $\Bbb R$-factorizable groups, Topology Proceedings 16 (1991), 201-231. (1991) | MR 1206464

Tkačenko M.G. Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37. (1991) | MR 1093863