A covering is said to be regular if for some $\displaystyle \widetilde{x_0} \in \widetilde{X}$ the group $\displaystyle p_{*} \ \pi ( \widetilde{X} , \widetilde{x_0} )$ is a normal subgroup of $\displaystyle \pi (X , x_0 )$. Prove that if $\displaystyle f$ is a closed path in $\displaystyle X$ then either every lifting of $\displaystyle f$ is closed or none is closed.