General Topology/Covering spaces

Note that more formally, one could have defined a covering space to be equal to a pair $(\tilde{X},\pi )$, where $\pi$ is the covering map that belongs to the covering space; indeed, many covering maps may be possible if $\pi$ is not specified. But as with group operations, we will mostly suppress $\pi$ from the notation for brevity.

When the domain of the function that is to be lifted is connected, then lifts are, in a certain sense, unique: