×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: EuDML