Locally minimal topological groups and their embeddings into products of $o$-bounded groups

Banakh, Taras O.. "Locally minimal topological groups and their embeddings into products of $o$-bounded groups." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 811-815. <http://eudml.org/doc/248581>.

@article{Banakh2000,
abstract = {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.},
author = {Banakh, Taras O.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\omega $-bounded group; $\sigma $-bounded group; $o$-bounded group; Weil complete group; locally minimal group; Lie group; topological group; complete group; locally minimal group; Lie group},
language = {eng},
number = {4},
pages = {811-815},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Locally minimal topological groups and their embeddings into products of $o$-bounded groups},
url = {http://eudml.org/doc/248581},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Banakh, Taras O.
TI - Locally minimal topological groups and their embeddings into products of $o$-bounded groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 811
EP - 815
AB - 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.
LA - eng
KW - $\omega $-bounded group; $\sigma $-bounded group; $o$-bounded group; Weil complete group; locally minimal group; Lie group; topological group; complete group; locally minimal group; Lie group
UR - http://eudml.org/doc/248581
ER -