About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Banakh, T.
Locally minimal topological groups and their embeddings into products of $o$-bounded groups. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 41 (2000), issue 4, pp. 811-815
MSC: 22A05, 22E15, 54H11 | MR 1800163 | Zbl 1049.54034
Keywords:
$\omega$-bounded group; $\sigma$-bounded group; $o$-bounded group; Weil complete group; locally minimal group; Lie group
Summary:
It is proven that an infinite-dimensional Banach space (considered as an Abelian topological group) is not topologically isomorphic to a subgroup of a product of $\sigma $-compact (or more generally, $o$-bounded) topological groups. This answers a question of M. Tkachenko.
References:
Gleason A.M.: Groups without small subgroups. Ann. Math. (1952), 56 193-212. MR 0049203 | Zbl 0049.30105
Guran I.: On topological groups close to being Lindelöf. Soviet Math. Dokl. 23 (1981), 173-175. Zbl 0478.22002
Hernández C.: Topological groups close to being $\sigma$-compact. Topology Appl. 102 (2000), 101-111. MR 1739266
Montgomery D., Zippin L.: Topological transformation groups. Interscience N.Y. (1955). MR 0073104 | Zbl 0068.01904
Tkachenko M.: Introduction to topological groups. Topology Appl. (1998), 86 179-231. MR 1623960 | Zbl 0955.54013
Partner of
EuDML logo