Lindelöf \(\Sigma\)-spaces and \(\mathbb R\)-factorizable paratopological groups (Q2422510)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lindelöf \(\Sigma\)-spaces and \(\mathbb R\)-factorizable paratopological groups |
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Lindelöf \(\Sigma\)-spaces and \(\mathbb R\)-factorizable paratopological groups (English)
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19 June 2019
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Summary: We prove that if a paratopological group \(G\) is a continuous image of an arbitrary product of regular Lindelöf \(\Sigma\)-spaces, then it is \(\mathbb R\)-factorizable and has countable cellularity. If in addition, \(G\) is regular, then it is totally \(\omega\)-narrow and satisfies \(\mathrm{cel}_\omega (G) \leq \omega\), and the Hewitt-Nachbin completion of \(G\) is again an \(\mathbb R\)-factorizable paratopological group.
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cellularity
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network
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\(G_\delta\)-diagonal group
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\(\mathbb R\)-factorizable group
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\(\omega\)-cellular group
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\(\omega\)-narrow group
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totally \(\omega\)-narrow group
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