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: