  The concept of gyrogroups is a generalization of groups which do not
explicitly have associativity. Recently, Atiponrat extended the idea of
topological (paratopological) groups to topological (paratopological)
gyrogroups. In this paper, we prove that every regular (Hausdorff) locally
gyroscopic invariant paratopological gyrogroup $G$ is completely regular
(function Hausdorff). These results improve theorems of Banakh and Ravsky for
paratopological groups. Also, we extend the Pontrjagin conditions of
(para)topological groups to (para)topological gyrogroups.
