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:Covering Map