Definition:Topological Covering Map

Definition

Let $E$ and $B$ be topological spaces.

Let $p: E \to B$ be a continuous surjection.

Then $p: E \to B$ is a covering map if every $b \in B$ has an open neighborhood whose preimage is a disjoint union of open sets such that the restriction of $p$ to each of them is a homeomorphism

That is:

Every $b \in B$ has an evenly covered open neighborhood.

Sources

• 2000: James R. Munkres: Topology (2nd ed.): $9$: The Fundamental Group $\S 53$: Covering Spaces