The regularity of quotient paratopological groups

Details The regularity of quotient paratopological groups The regularity of quotient paratopological groups

2010-03-29

arxiv.org/abs/1003.5409v1

Mathematics

Group Theory

6 pages

Scientific paper

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, weaker that 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.

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