The regularity of quotient paratopological groups

Author
T. Banakh1, A. Ravsky2
1) Department of Mathematics, Ivan Franko Lviv National University Lviv, Ukraine; 2) Department of Functional Analysis Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine Lviv, Ukraine
Abstract
Let $H$ be a closed subgroup of a regular Abelian paratopological group $G$. The group reflexion $G^\flat$ 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 $G^\flat$. 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.
Keywords
paratopological group; quotient paratopological group; group reflexion; regularity
DOI
doi:10.15330/ms.49.2.144-149
Reference
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Pages
144-149
Volume
49
Issue
2
Year
2018
Journal
Matematychni Studii
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