Exercise 12, § 2

Let $G$ be a semi-topological (resp. paratopological, quasi-topological) group and let $H$ be a normal subgroup of $G$.

a) Show that if $G/H$ is endowed with the quotient topology of $G$ by $H$, then $G/H$ is a semi-topological (resp. paratopological, quasi-topological) group.

b) Extend the results of no. 7 to semi-topological (resp. paratopological, quasi-topological) groups.