Quasi-uniformities and quotients of paratopological groups

If $H$ is a subgroup of a paratopological group $G$ , we prove that the quotient topology of the coset space $G/H$ is induced by a point-rotund uniformity and the quotient topology of the semiregularization $(G/H)_{sr}$ of $G/H$ is induced by a normal quasi-uniformity. In particular, $(G/H)_{sr}$ is a Tychonoff space provided that $G/H$ is Hausdorff . The previous results are applied in order to show that every Hausdorff Lindel o f paratopological group is $\omega$ -admissible. We also show that, if $G$ is an $\omega$ -admissible paratopological group, then so is the reflections $T_i(G)$ (i=1,2,3), $Reg(G)$ and $Tych(G)$ .