\begin{definition}[Definition:Evenly Covered]
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 $U$.
\end{definition}