Definition:Evenly Covered

Definition

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

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

An open set $U \subset B$ is evenly covered by $p$ if its preimage is a disjoint union of open sets such that the restriction of $p$ to each of them is a homeomorphism to $U$.

Also see

• Definition:Topological Covering Map

Sources

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