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

Taras O. Banakh

Displaying similar documents to “Locally minimal topological groups and their embeddings into products of $o$ -bounded groups”

Homomorphic images of $ℝ$ -factorizable groups

Mihail G. Tkachenko (2006)

Commentationes Mathematicae Universitatis Carolinae

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It is well known that every $ℝ$ -factorizable group is $ω$ -narrow, but not vice versa. One of the main problems regarding $ℝ$ -factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every $ω$ -narrow group is a continuous homomorphic image of an $ℝ$ -factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an $ℝ$ -factorizable...