  In this paper, we consider the continuity of the inverse in (strongly)
paratopological gyrogroups. The conclusions are established as follows: (1) A
compact Hausdorff paratopological gyrogroup $G$ is a topological gyrogroup. (2)
A Hausdorff locally compact strongly paratopological gyrogroup is a topological
gyrogroup. (3) If $G$ is locally compact strongly paratopological
gyrocommutative gyrogroup (without any separation restrictions), then $G$ is a
strongly topological gyrogroup. (4) Every regular feebly compact strongly
paratopological gyrogroup is a topological gyrogroup. (5) If a Hausdorff
strongly paratopological gyrogroup $G$ is countablly compact and topologically
periodic, then $G$ is a strongly topological gyrogroup.
