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Taras Banakh

Locally minimal topological groups and their embeddings into products of

o

-bounded groups

Comment.Math.Univ.Carolinae 41,4 (2000) 811-815.

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 σ-compact (or more generally, o-bounded) topological groups. This answers a question of M. Tkachenko.

Keywords: ω-bounded group,σ-bounded group,o-bounded group, Weil complete group, locally minimal group, Lie group

AMS Subject Classification: 22A05, 54H11

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