This is really interesting. Why does the failure of naive parameterizations to form a cover imply a group with gimbal lock? I'm unclear on how a cover is linked

This is really interesting. Why does the failure of naive parameterizations to form a cover imply a group with gimbal lock? I'm unclear on how a cover is linked to gimbal lock. I've taken undergrad topology and algebra if you could explain in those terms (I understand what a covering is).