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

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.

Keywords: $\omega $-bounded group, $\sigma $-bounded group, $o$-bounded group, Weil complete group, locally minimal group, Lie group
AMS Subject Classification: 22A05, 54H11

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