The regularity of quotient paratopological groups

Original · EN

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, 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. 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.