# Definition:Evenly Covered

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## 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

## Sources

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