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Subgroups of $$\mathbb R$$-factorizable groups. (English) Zbl 0937.54023
A topological group is called $$\mathbb R$$-factorizable if for every continuous function $$g:G\to \mathbb R$$ there exist a continuous homomorphism $$\pi :G\to H$$ of $$G$$ onto a second-countable topological group $$H$$ and a continuous function $$h:H\to \mathbb R$$ such that $$g=h\pi$$. There is proved that a locally compact group $$G$$ is $$\mathbb R$$-factorizable iff $$G$$ is $$\sigma$$-compact.
Reviewer: J.Rosický (Brno)

##### MSC:
 54H11 Topological groups (topological aspects) 22A05 Structure of general topological groups
##### Keywords:
topological group; $$\mathbb R$$-factorizable group
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