Covering Space

In algebraic topology, a covering space of a space $X$ is a space $\tilde{X}$ together with a map $p:\tilde{X}\to X$ such that: For each $x\in X$, there exists open neighborhood $U$ of $x$ in $X$ such that $p^{-1}U$ is a union of disjoint open sets of which is mapped homeorphically onto $U$ by $p$.

Sources

Copied from hatcher2001-algebraic-topology, chapter 1.