The regularity of quotient paratopological groups
Journal Title: Математичні Студії - Year 2018, Vol 49, Issue 2
Abstract
Let H be a closed subgroup of a regular Abelian paratopological group G. The group reflexion G♭ of G is the group G endowed with the strongest group topology, which is weaker than the original topology of G. We show that the quotient G/H is Hausdorff (and regular) if H is closed (and locally compact) in G♭. On the other hand, we construct an example of a regular abelian paratopological group G containing a closed discrete subgroup H such that the quotient G/H is Hausdorff but not regular.
Authors and Affiliations
Taras Banakh, A. Ravsky
Keywords
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- EP ID EP411743
- DOI 10.15330/ms.49.2.144-149
- Views 51
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